Answer:
AB is not tangent to the circle.
Step-by-step explanation:
A tangent is a straight line that touches a circle at only one point.
The tangent of a circle is always perpendicular to the radius.
Therefore, if AB is tangent to the circle, it will form a right angle with the radius, CA.
To determine if AB is tangent, we can use Pythagoras Theorem.
\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)
If AB is tangent, then angle CAB will be a right angle. So AC and AB would be the legs of the right triangle, and BC would be the hypotenuse.
Therefore:
\(AC^2+AB^2=BC^2\)
Substitute the values into the equation:
\(7^2+12^2=15^2\)
\(49+144=225\)
\(193 = 225 \; \leftarrow\; \sf not\;true\)
As 193 ≠ 225, the equation does not hold, hence proving that AB is not tangent to the circle.
what is the next two terms of the sequence 12,17,22,27
Answer:
32 and 37
Step-by-step explanation:
Because the difference between the values is 5.
Please answer this correctly
Answer
51
Explanation
85/15=y/9
765=15y
51
Answer:
y = 51
Step-by-step explanation:
These triangles are similar, so you can set up a proportion to solve for y:
\(\frac{85}{15} =\frac{y}{9}\)
Cross multiply:
\(\frac{765}{15y}\)
Divide 765 by 15:
y = 51
Explain in detail using words the step by step process that Maggie took to solve the problem 6.89 x 10^-4 / 7.5 x 10^-6 = .92 x 10^1
The steps in solving the given expression shows that the result is:
0.92 * 10²
How to use Laws of Exponents?The expression is given as:
6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹
The steps that Maggie followed are:
Step 1: Rewrite the given expression:
6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹
Step 2: Divide the coefficients:
The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:
6.89 / 7.5 = 0.9186667.
Step 3: Divide the powers of 10:
This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²
Step 4: Combine the results:
This gives:
0.9186667 * 10²
Step 5: Simplify the coefficient:
She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.
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Adama rolls a die with faces labeled 1 through 10. If he rolls the die 40 times how many times would he expect it to land on a number less than 10?
Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.
The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.
The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.
The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.
Therefore, the expected number of times the die will land on a number less than 10 is:
E = (9/10) x 40 = 36
Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.
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☆ 36 times.
— your in college ? im in seventh grade and got this question !
onsider the line =+7x5y−4. Find the equation of the line that is parallel to this line and passes through the point −−4, 5. Find the equation of the line that is perpendicular to this line and passes through the point −−4, 5.
The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is y = -7/5(x) -53/5
How to find the equation of the lines parallel and perpendicular to 7x+5y = 4?Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)
The slope-intercept form of a straight line is:
y = mx + c
where m is the slope and c is the y-intercept
For perpendicular case:
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₁ x m₂ = -1
-7/5 x m₂ = -1
m₂= 5/7
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = 5/7 (-4) + c
-5 = -20/7 + c
c = -15/7
Thus, the equation of the line is y = 5/7(x) -15/7
For parallel case:
When the two lines are parallel, they have equal slope i.e. m₁ = m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₂= -7/5
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = -7/5(-4) + c
-5 = 28/5 + c
c = -53/5
Thus, equation of the line is y = -7/5(x) -53/5
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if 6 people can walk 12 dogs, how many people are needed to walk 24 dogs
Answer:
12 people are need to walk 24 dogs
Step-by-step explanation:
12/2=6
24/2=12
Answer:
12 people can walk 24 dogs.
Step-by-step explanation:
Given information,
→ 6 people can walk 12 dogs.
→ People required for 24 dogs = ?
Let us assume that,
→ Missing value = p
Forming the equation,
→ 6/12 = p/24
Then the value of p will be,
→ 6/12 = p/24
→ p/24 = 6/12
→ p × 12 = 6 × 24
→ 12p = 144
→ p = 144/12
→ [ p = 12 ]
Hence, the value of p is 12.
Ques- Explain the concept of maximum value function.
Seymour has 5 candy bars that he would like to split equally among 4 children. How much candy will each child get?
u diviide the number of candies by the number of people
Step-by-step explanation:
5/4
Answer:
Each child would get 1 1/4 of a candy bar
Step-by-step explanation:
If Seymour is 1 out of 4 kids and has 5 candy bars each kid gets 1 candy bar (4 candy bars) and then there is 1 candy bar remaining. This 1 candy bar can then be split into 1/4ths so each kid gets 1 1/4 candy bars.
Please help! 25 points!!
The final expression of the inequality will be b≤15.
What is inequality?
Inequalities in mathematics are expressed as mathematical expressions containing inequalities on both sides. Instead of using equations, we compare two values while analysing an inequality. The equal sign is replaced in between by the not equal to, greater than, or less than (or less than or equal to) signs.
Olivia gets a spot on the 12U softball squad. How old is Olivia? You don't know how old Olivia is because it doesn't say "equals." However, you can write Olivia's age as 12 as you already know she is under or equal to that age. This hypothetical situation pertains to inequality in the actual world.
Given expression is b/3 ≤ 5
Here we can multiply with 3 on both sides
b ≤ 5*3
b≤15
Hence The final expression of the inequality will be b≤15.
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Read the following paragraph and answer the question. "Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992 doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects." What is the main purpose of this
paragraph?
A. To inform the reader of a subject
B. To persuade by sharing a perspective about a subject
C. To entertain the audience
The main purpose of this paragraph is to inform the reader of a subject.
What is reading paragraph?Reading paragraph is the ability to process text, understand its meaning, and to integrate with what the reader already knows.
Given is a passage, about an American Screenwriter and author, Emest Cline,
The paragraph is telling about life of the author, telling about his works, the latest, first, the most successful works, his birthplace, etc. but every thing about him.
Simply, if we see, this tell us the information related to the subject who is Emest Cline,
Hence, the main purpose of this paragraph is to inform the reader of a subject.
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Write the equation of the line, in all three forms, that is parallel to the line that passes through the points (-6, 1) and (10,0) and passes through point (-7,-2).
The linear equation parallel to the line that passes through (-6, 1) and (10,0) and that passes through (-7, -2) is:
y = (-1/16)*x - 39/16
How to find the linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept
If a linear equation crosses through two known points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:
a = (y₂ - y₁)/(x₂ - x₁)
And two lines are parallel if and only the two lines have the same slope and different y-intercept.
Here we want to find a line that passes through (-6, 1) and (10, 0), the slope of that line is:
a = (0 - 1)/(10 + 6) = -1/16
And we want to find a line with this slope that passes through the point (-7, -2), so we need to have:
-2 = (-1/16)*-7 + b
-2 = 7/16 + b
-2 - 7/16 = b
-32/16 - 7/16 = b
-39/16 = b
So the linear equation is:
y = (-1/16)*x - 39/16
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Function g is defined by g(x) = 3(x + 8). What is the value of g(12)?
Answer:
g(12) = 60Step-by-step explanation:
\(g(x) = 3(x + 8)\)
To find g(12) , substitute the value of x that's 12 into g(x). That is for every x in g(x) replace it with 12
We have
\(g(12) = 3(12 + 8) \\ \: \: \: \: = 3(20)\)
We have the final answer as
g(12) = 60Hope this helps you
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
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For what value of A is the function, (x), continuous at x=0?
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
\(\lim_{x \to 0}\) h(x) = h(0)
\(\lim_{x \to 0}\) x cos x/sin λx = 1/7
\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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Choose a reasonable estimate for the amount of water a cup would hold.
Answer:
A cup of water can hold a cup of water (or about 250 mL)
Step-by-step explanation:
anything between 1 and 4 cups should be an acceptable answer
If this helps, please consider giving me brainliest
Answer:
I'm gonna go with 250 ML
Step-by-step explanation:
One liter is a little more than 1 quart.
250 mL = 0.25 L
I NEED HELP!! I'll give you brainliest!! A high school wants to expand its P.E. schedule. To better understand the needs of the students, the principal looked at which forms of exercise are preferred by the 18 students in the sample group.The Venn Diagram shows this information be gathered.a. How many students preferred swimming over running or walking?b. How many students choose running or walking?c. Which students preferred swimming and walking, but not running
Answer:
a. Three students preferred swimming over running and walking.
b. Fourteen students chose running or walking.
c. Alex and Jose preferred swimming and walking, but not running.
PLEASE HELP ME PLEASE
Question 6 of 10
f(x) = 5x + 1) – 3
g(x) = 4
Find (f - g)(x).
Answer:
Answer:
5x + 6
Step-by-step explanation:
(f-g)(x) is nothing but f(x) - g(x)
f(x) is |5x + 1| - 3 and g(x) is 4 so the equation is [|5x+1| - 3] - [4]
Once this is solved, the answer is 5x - 6. Since there's absolute value, remove the negative and change it to a positive to get the answer 5x + 6.
1(a). Find the work done by a truck driver to load a box of
40lb to the truck bed 3 ft high.
1 (b). If he took 5 seconds to load the box, what was the power
delivered.
In physics, work is energy transferred to or from an object by applying a force along a displacement and the work done in the given situation is 120J.
What do we mean by work?In physics, work is energy transferred to or from an object by applying a force along a displacement.
In its simplest form, work done with a constant force in the direction of motion is equal to the product of the force and the distance traveled.
Expressing this concept mathematically, the work W is equal to the force f multiplied by the distance d, or W = fd.
If the force is applied at an angle θ to the displacement, the work done is W = fd cos θ.
So, the work done is calculated as follows:
W = 40lb*3ft
W = 120 J
Therefore, the work done in the given situation is 120 J.
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PLEASE HELP DUE IN 1 HOUR
The 3rd and 4th expressions cannot be simplified using the quotient rule for exponents
How to determine expressions that cannot be simplified using the quotient rule for exponents?The quotient rule for exponents states that if you have two exponents, and you want to divide them, you can do so by subtracting the exponent of the denominator from the exponent of the numerator.
The general form of the quotient rule:
xᵃ / xᵇ = xᵃ⁻ᵇ
Given:
(3²9⁻¹2³)/(8⁵7⁻²)
(3²9⁻¹2³)/(8⁵7⁻²) = (3² × 3²⁽⁻¹⁾ × 2³)/(8⁵×7⁻²)
= (3² × 3⁻² × 2³)/(2³⁽⁵⁾ ×7⁻²)
= (3²⁺⁽⁻²⁾ × 2³)/(2¹⁵ × 7⁻²)
= (3⁰ × 2³)/(2¹⁵ × 7⁻²)
= (1 × 2³)/(2¹⁵ × 7⁻²)
= (2³)/(2¹⁵ × 7⁻²)
= 2³⁻¹⁵ × 7² ( quotient rule is used here)
= (2⁻¹²) (7²)
(4⁻²x⁻¹)/(4⁻¹x⁻²)
(4⁻²x⁻¹)/(4⁻¹x⁻²) = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾ ( quotient rule is used here)
= 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾
= (4⁻¹) (x¹)
(6x⁻⁸z²)(6⁵x⁻¹z²)
(quotient rule cannot be used to simplify this expression because the two expressions are multiplying each other)
(q⁻⁵r¹¹)/(s⁶t⁻¹⁵)
(quotient rule cannot be used here because there are no like bases)
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What is (f−g)(x)? f(x)=3x5+6x2−5 g(x)=2x4+7x2−x+16
Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16
(f-g)(x)= 3x⁵-2x⁴-x²+x-21
Step-by-step explanation:
Here we have,
Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16
We know,
(f-g)(x)= f(x)-g(x)
= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)
On subtracting g(x) from f(x) we get,
(f-g)(x)= (3x⁵+6x²-5 - 2x⁴-7x²+x-16)
On simplify,
(f-g)(x) =3x⁵-2x⁴-x²+x-21
Hence,
(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21
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Mr. Darson bought 6 boxes of nails from a shop. Each box had an equal number of nails. He gave 8 nails to each of his 38 students. He then had 26 nails left. Find the number of nails in each box.
Answer:55 nail boxes
Step-by-step explanation: first we have to find out the total amount of nails in all the boxes so for this we do 38*8=304
when he gave all the nails to all his students he has 26 extra nails left. so we add this amount to the original which gives us 330 total nails.
to find out the number of nails in eadh box we divide 330/6=55
The equation -3( x-3) -1 = ax + b have infinite amount of solutions?
The equation given in the task content; -3 ( x-3) -1 = ax + b will have infinite amount of solutions if; a = -3 and b = 8.
What equations have infinitely many solutions?It follows from the task content the condition form which the equation given would have infinite amount of solutions be determined.
Recall that a linear equation; mx + p = nx + r is said to have infinite amount of solutions if; m = n and p = r.
Therefore, by evaluation of the given equation; -3( x-3) -1 = ax + b; we have;
-3x + 9 - 1 = ax + b
-3x + 8 = ax + b
Consequently, the equation is said to have infinitely many solutions if; a = -3 and b = 8.
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who is good at accounting I need some help
Answer:
Accounting is the process of recording financial transactions pertaining to a business. ... The financial statements used in accounting are a concise summary of financial transactions over an accounting period, summarizing a company's operations, financial position, and cash flows.
Step-by-step explanation:
What is the length of Line segment A C? Round to the nearest tenth.
Answer:
wheres the info
Step-by-step explanation:
Answer:
A: 10.5 m
Step-by-step explanation:
i think it's A, i may be wrong! hope this helps!!~
You want to share 1000 dollars between you and 5 friends,
Can you share the money evenly
What is the maximum amount that can be shared evenly
What is then the leftover as a fraction
Answer:
the answer is 200
Step-by-step explanation:it's because
you have to divide 1000 in to 5 and 1000 divided by 5 is 200
Alvin is 12 years younger than Elga. The sum of their ages is 28. What is Elga's age?
Answer:
Step-by-step explanation:
i think its 16
Evaluate when
a =3 b= 4.5 and h = 6
Answer:
For Example: Evaluate a2b for a = –2, b = 3, c = –4, and d = 4.
Step-by-step explanation:
To find my answer, I just plug in the given values, being careful to use parentheses, particularly around the "minus" signs. Especially when I'm just starting out, drawing the parentheses first may be helpful:
a2 b
( )2 ( )
(–2)2 (3)
(4)(3)
12
Note how using parentheses helped me keep track of the "minus" sign on the value of a. This was important, because I might otherwise have squared only the 2, ending up with –4, which would have been wrong.
By the way, it turned out that we didn't need the values for the variables c and d. When you're given a big set of expressions to evaluate, you should expect that there will often be one or another of the variables that won't be included in any particular exercise in the set.
Evaluate a – cd for a = –2, b = 3, c = –4, and d = 4.
In this exercise, they've given me extra information. There is no b in the expression they want me to evaluate, so I can ignore this value in my working:
(–2) – (–4)(4)
–2 – (–16)
–2 + 16
16 – 2
14
PLEASE HELP THIS IS DUE TODAY
In conclusion the value that correctly fills in the blank in the table is 0.69.
Why it is?
To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.
We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):
Relative frequency for boys = (40 + 43) / 120 ≈ 0.69
Rounding to the nearest hundredth, we get:
Relative frequency for boys ≈ 0.69
Therefore, the value that correctly fills in the blank in the table is 0.69.
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Choose the system of inequalities that best matches the graph below.
Answer: D
Step-by-step explanation:
Hope it helps