Which statement about BC←→ is correct?
BC←→ is a tangent line because △ABC is a right triangle.
BC←→ is a tangent line because the sum of the angles in △ABC is 180º.
BC←→ is not a tangent line because m∠ABC≠90°.
BC←→ is a tangent line because m∠ABC is acute.
Answers
So a tangent line is perpendicular to the radius, which means it creates a 90 degree angle with the radius of the circle. The sum of the interior angles of any triangle is 180 degrees. To determine if line BC is a tangent line, we have to determine if angle ABC is 90 degrees. Well we know the degrees of the other two angles of the triangle, so let's set up an equation:
180 = 48 + 47 + x
180 = 95 + x
85 = x
Since angle ABC must be 85 degrees (not 90), line BC is not a tangent line.
Answer:
BC←→ is not a tangent line because m∠ABC ≠ 90°.
The measure of angle at the tangent of a circle is a right angle.
The correct statement about BC is (c) BC is not a tangent line because m∠ABC≠90°.Start by calculating the measure of angle ABC using the following angle in a triangle theorem
[tex]\angle ABC + 48 + 47 = 180[/tex]
[tex]\angle ABC + 95 = 180[/tex]
Subtract 95 from both sides of the equation
[tex]\angle ABC = 180 - 95[/tex]
[tex]\angle ABC = 85[/tex]
For line BC to be a tangent, then the following must be true
[tex]\angle ABC = 90[/tex]
Hence, the correct statement about BC is (c)
Read more about tangent lines at:
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Related Questions
Suppose we set θ0=−2,θ1=0.5 in the linear regression hypothesis from q1. what is hθ(6)?
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hθ(x) = -2 + 0.5x
hθ(6) = -2 + 0.5 * 6
hθ(6) = 1
Ben brought two pizzas to a party. He says that sinceramente 1/4 of each pizza is left,the sale a Mountain of each pizza is left. What is his error?
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Final answer:
Ben incorrectly assumed that ¼ of two pizzas combined would still be ¼; however, the correct sum is ¼ + ¼ which equals ½ of a pizza. To add fractions, only the numerators are added when denominators match. Mastery of fractions is critical in both academics and day-to-day life.
Explanation:
Ben's error lies in the misunderstanding of fractions and how they add up. If Ben has two pizzas and each has ¼ left, combining the two portions does not result in having ½ of a pizza, but instead, he would have ¼ + ¼ which equals ½. This is because when adding fractions, you only add the numerators (the top numbers) if the denominators (the bottom numbers) are the same. Therefore, ¼ of one pizza plus ¼ of another pizza would equal ½ of a pizza. It's important to understand that fractions represent parts of a whole and that these parts must be added correctly to find the total amount.
Being comfortable with fractions is important not only for academic success but also for everyday life, such as understanding discounts, following recipes, or splitting bills. Utilizing real-life examples like these can help strengthen one's intuitive sense of fractions and make mathematical concepts more relatable.
is (0,0) a solution to this system? y ≥ x^2 + x - 4, y> x^2 + 2x + 1
Answers
Final Answer:
The point (0,0) does not satisfy the inequality [tex]y ≥ x^2[/tex] + x - 4, as 0 is not greater than or equal to -4. Additionally, it does not satisfy [tex]y > x^2 + 2x + 1[/tex], as 0 is not greater than 1. Therefore, (0,0) does not meet the conditions of the system of inequalities.
Step-by-step explanation:
The point (0,0) is not a solution to the given system of inequalities. First, considering the inequality [tex]y ≥ x^2 + x - 4[/tex], when substituting x=0 and y=0 into the equation, we find that 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the conditions of the first inequality. Moving on to the second inequality, [tex]y > x^2 + 2x + 1[/tex], substituting x=0 and y=0 results in 0 not being greater than 1.
Consequently, (0,0) fails to meet the requirements of the second inequality as well. In summary, the point (0,0) does not simultaneously satisfy both inequalities, rendering it unsuitable as a solution to the system.
Analyzing solutions to systems of inequalities involves evaluating each inequality independently to ensure the chosen point satisfies all conditions. In this instance, the failure of (0,0) to satisfy either inequality demonstrates that it does not conform to the system's criteria. When dealing with systems of inequalities, it is essential to carefully assess each component to accurately determine the solution set.
No, (0,0) is not a solution to the given system.
Explanation:The system consists of two inequalities: y ≥ x^2 + x - 4 and y > x^2 + 2x + 1. To check whether (0,0) is a solution, substitute x = 0 and y = 0 into both inequalities. For the first inequality, x^2 + x - 4 becomes -4, and 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the first inequality. Moving on to the second inequality, x^2 + 2x + 1 becomes 1, and 0 is not greater than 1. Hence, (0,0) fails to satisfy the second inequality as well. As a result, (0,0) is not a solution to the system of inequalities.
In summary, by substituting the coordinates of (0,0) into both inequalities, we find that the point does not meet the conditions set by either inequality. Therefore, (0,0) is not a solution to the system. This conclusion is based on the specific values obtained through substitution, demonstrating that the coordinates do not satisfy the given inequalities.
Pepe is putting a fence in his backyard to enclose the garden in form of a triangle. The garden already has sides enclosed with 8 feet and 5 feet of fence, respectively. What can you say about the length of the third side?
Answers
[tex] a^{2} [/tex] + [tex] b^{2} [/tex] = [tex] c^{2} [/tex]
Let a = 8.
Let b = 5.
We must find c to determine the length of the third side of the triangle. To find c, we can substitute the values that we are already know, and solve for c:
[tex] 8^{2} [/tex] + [tex] 5^{2} [/tex] = [tex] c^{2} [/tex]
64 + 25 = [tex] c^{2} [/tex]
89 = [tex] c^{2} [/tex]
[tex] \sqrt{89} [/tex] = c
9.43 = c
This means that the length of the third side of the fence in the garden is 9.43 feet.
Answer:
Step-by-step explanation:
Pepe is putting a fence in his backyard to enclose the garden in the form of a triangle.
In the garden already has sides enclosed with 8 feet and 5 feet.
We know a triangle is possible when sum of length of two sides > third side
so third side < 8 + 5
or third side should be less than 13.
find the nonpermissible replacement for y in this expression Y+7/Y-3
Answers
Final answer:
The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.
Explanation:
The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.
Steps to find the nonpermissible value:
Identify the denominator of the expression, which is (Y-3).
Set the denominator equal to zero: Y - 3 = 0.
Solve for y: Y = 3.
Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.
Which unit should be studied to review symbols from set theory? Unit 1 Unit 3 Unit 5 Unit 7
Answers
A human gene carries a certain disease from the mother to the child with a probability rate of 70%. suppose a female carrier of the gene has three children. also assume that the infections of the three children are independent of one another. find the probability that at least one child gets the disease from their mother.
Answers
P(X ≥ 1) = 1 - P(X = 0). This is because the only choice other than at least one child inheriting the disease is that no children get it.
Since there is a 70% or 0.7 chance that each child will inherit it, there is a 30% or 0.3 chance that they will not. This gives us
1 - P(X = 0) = 1 - (0.3)(0.3)(0.3) = 1 - 0.027 = 0.973
There is a 97.3% chance that at least one of the children will get the disease from their mother.
The probability that at least one of the three children gets the disease from their mother is 97.3%.
To find the probability that at least one child gets the disease from their mother when a female carrier of the gene has three children, we can follow these steps:
1. Define the probabilities:
- Probability that a child gets the disease from their mother (given): [tex]\( P(D) = 0.70 \)[/tex].
- Probability that a child does not get the disease from their mother: [tex]\( P(D^c) = 1 - P(D) = 0.30 \)[/tex].
2. Identify the total number of children:
- Number of children: [tex]\( n = 3 \)[/tex].
3. Calculate the probability that none of the children get the disease:
- For all three children to not get the disease, the probability is [tex]\( (P(D^c))^n = (0.30)^3 \)[/tex].
4. Find the probability that at least one child gets the disease:
- The probability that at least one child gets the disease is the complement of the probability that none of the children get the disease.
- Thus, [tex]\( P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) \)[/tex].
Let's do the calculations step by step.
Step-by-Step Calculations:
1. Calculate the probability that none of the children get the disease:
[tex]\[ P(\text{none of the children get the disease}) = (P(D^c))^3 = (0.30)^3 \][/tex]
2. Perform the exponentiation:
[tex]\[ (0.30)^3 = 0.30 \times 0.30 \times 0.30 = 0.027 \][/tex]
3. Calculate the probability that at least one child gets the disease:
[tex]\[ P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) = 1 - 0.027 = 0.973 \][/tex]
Conclusion:
The probability that at least one child gets the disease from their mother is [tex]\( 0.973 \)[/tex], or 97.3%.
helpppppppppppppppppppppp
Answers
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
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At an amusement park, the probability that a child eats a hot dog and drinks a soda pop is 0.38. The probability that a child eats a hot dog is 0.61, and the probability that a child drinks soda pop is 0.89. What is the probability (rounded to the nearest hundredth) that a child drinks soda pop given that the child has already eaten a hot dog? Hint: cap p left parenthesis cap a vertical line cap b right parenthesis equals start fraction cap p left parenthesis cap a intersection cap b right parenthesis over cap p left parenthesis cap b right parenthesis end fraction
A| 0.34
B| 0.43
C| 0.62
D| 0.69
Answers
If a company is considering the purchase of a parcel of land that was acquired by the seller for $93,000 is offered for sale at $166,000, is assessed for tax purposes at $103,000, is recognized by the purchaser as easily being worth $156,000, and is purchased for $153,000, the land should be recorded in the purchaser's books at:
Answers
Answer:
The land should be recorded in the purchaser's books at : $153,000.
Step-by-step explanation:
Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.
Evaluate the expression. If necessary, round to the nearest hundredth.
log 1,000
3
103
1/3
Answers
3 is the correct answer.
[tex] log(1000) = log_{10}( {10}^{3} ) = 3 [/tex]
So the answer to your question is 3.
A cone with volume 5000 m³ is dilated by a scale factor of 15. What is the volume of the resulting cone? Enter your answer in the box. m³
Answers
Answer:
[tex]40\ m^{3}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> scale factor
x-----> the volume of the dilated cone
y-----> the volume of the original cone
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=1/5[/tex]
[tex]y=5,000\ m^{3}[/tex]
substitute and solve for x
[tex](1/5)^{3}=\frac{x}{5,000}[/tex]
[tex](1/125)=\frac{x}{5,000}[/tex]
[tex]x=5,000/125=40\ m^{3}[/tex]
Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How far apart are Jacob and Sharon now?
Answers
Consider the coordinate plane:
1. The origin is the point where Sharon and Jacob started - (0,0).
2. North - positive y-direction, south - negetive y-direction.
3. East - positive x-direction, west - negative x-direction.
Then,
if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).The distance between two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be calculated using formula
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]
Therefore, the distance between Jacob and Sharon is
[tex]D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.[/tex]
What is the circumference of the circle in terms of pi? The radius is 2.2 and I got 13.82 but the choices are 1.1, 1.21, 2.2 and 4.4 im so confused so could someone please explain what i did wrong?
Answers
C = 2 π (2.2)
C = 4.4 π (in term of pi)
answer
4.4π
The simplest form of square root of eighty can be written as a times square root of b, where a = and b = .
Answers
The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
Fuel prices have increased by 9% this year. The smiths family’s fuel bill for this year is now £1956. How much was the bill likely to have been last year
Answers
1956 times .09 equals 176.04, subtract 176.04 fro 1956 and you get 1779.96.
an internet company charges a one time setup fee of 44.99 and a monthly fee of 29.99 for internet service the company is offering a 25 percent discount on the monthly fee for the first year
Answers
yark
Which ratios form a proportion?
3/15, 12/55
8/24, 12/35
5/18, 25/90
4/11, 16/25
What ratio forms a proportion with 9/15?
6/10
16/21
36/50
45/70
Answers
Answer: 1. C) 5/18, 25/90
2. A) 6/10
Step-by-step explanation: 1) We need to find the ratios those makes a proportion:
Let us check given options one by one.
3/15, 12/55
Converting them into simplest fractions.
3÷3/15÷3 = 1/5
12/55 can't be reduce more.
1/5 ≠ 12/55
So, 3/15, 12/55 don't form a proportion.
8/24, 12/35
Converting them into simplest fractions.
8÷8/24÷8 = 1/3
12/35 can't be reduce more.
8/24 ≠ 12/35
So, 8/24, 12/35 don't form a proportion.
5/18, 25/90Converting them into simplest fractions.25÷5/90÷5 = 5/18 5/18 can't be reduce more.5/18 = 5/18.So, 8/24, 12/35 don't form a proportion.
So, 5/18, 25/90 form a proportion.
4/11, 16/25
Converting them into simplest fractions.
4/11 and 16/25 both can't be reduce more.
4/11≠16/25
So, 4/11, 16/25 don't form a proportion.
___________________________________________________
Let us reduce 9/15 into simplest fraction.
9÷3/15÷3 = 3/5Now, let us convert each and every option in simplest fractions.
6÷2/10÷2 = 3/516÷1/21÷1 = 16/21
36÷2/50÷2 = 18/25
45÷5/70÷5 = 9/14
We can see 6/10 gives lowest fraction 3/5 as 9/15 gives.
Therefore, 6/10 form a proportion with 9/15.
.hey can you help me I will crown you brainliest
Answers
please help thank you
Answers
When doing ratios, if you know the proportion of the length and width you just multiply that ratio to the origingal value
What is the x-intercepts of the graph of y = 12x-5x-2
Answers
First, we see that it's already written in slope intercept, y = mx + b where m is the slope and b is the y intercept, we just need to simplify the like terms on the right. We have:
y = 12x-5x-2
y = 7x - 2
Now that we have it in slope intercept form, whenever we have an x intercept, since it is crossing the x axis, there's no y value. We plug in 0 for y:
0 = 7x - 2
2 = 7x
2/7 = x
The x intercept is (2/7, 0)
Hope this helps!
There's a 40% chance of rain on Tuesday and a 50% chance of rain Friday. What percent will it rain both Tuesday and Friday?
p.s. this is a probability question I think
Answers
50% or 50/100 which is in decimal format 0.5.
P( tueday AND friday) <----- AND is a keyword, means product
P(tuesday) AND P(friday)
0.4 * 0.5
0.2 or 0.2 * 100 or 20% chance that it will rain on both days.
Write an equation that is perpendicular to y = -7x + 2 and passes through (7 , 5)
Answers
The slope of a line perpendicular to another line is the negative reciprocal, that is, [tex]m_{perp} = \frac{-1}{m} [/tex].
For your equation, the slope is –7. That means the slope of its perpendicular line must be [tex]- \frac{-1}{7} = \frac{1}{7} [/tex].
Now, we must also find such a line that passes through (7, 5). It is easiest to write this in point-slope form, [tex]y-y_1=m(x-x_1)[/tex].
We get [tex]y-5= \frac{1}{7} (x-7)[/tex]. Technically, we are done, but it is customary to convert this into slope-intercept form, [tex]y=mx+b[/tex].
[tex]y-5= \frac{1}{7} (x-7)\\\\y= \frac{1}{7}x-1+5\\\\y= \frac{1}{7}x+4[/tex].
And that's our final answer. We can verify the solution graphically. See attached.
In general, our steps are:
1) Find the slope of the given line if it is not given directly.
2) Find the slope of the perpendicular line (the negative reciprocal).
3) Identify the point it must pass through.
4) Substitute the values into the point-slope form.
5) Write the equation in slope-intercept form.
Find the constant rate of change for each linear function and interpret their meaning.
Answers
simplify this expression. (√2 + √3)(√5 - √7)
Answers
The simplified expression is √10 - √14 + √15 - √21.
To simplify the expression (√2 + √3)(√5 - √7), we can use the distributive property of multiplication.
Expanding the expression, we get:
(√2 + √3)(√5 - √7) = √2 x √5 + √2 x (-√7) + √3 x √5 + √3 x (-√7)
Now, simplifying each term with FOIL method we have:
√2 * √5 = √(2 x 5) = √10
√2 * (-√7) = -√(2 x 7) = -√14
√3 * √5 = √(3 x 5) = √15
√3 * (-√7) = -√(3 x 7) = -√21
Combining the simplified terms, we get:
√10 - √14 + √15 - √21
Therefore, the simplified expression is √10 - √14 + √15 - √21.
In this process, we applied the distributive property to expand the expression and then simplified each term by multiplying the square roots together. Finally, we combined the like terms to obtain the simplified expression.
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Answer:
√10 + √15 - √14 - √21
Step-by-step explanation:
(√2 + √3)(√5 - √7)
= √2(√5 - √7) + √3(√5 - √7)
= √10 - √14 + √15 - √21
= √10 + √15 - √14 - √21
Given the geometric sequence 100, 50, 25, ..., find the 7th term.
Answers
T(7)=100(1/2)^6=1.5625
What should I do ???
Answers
For example, to find the area of problem number 1, I would multiply 8 (length) times 2 (width) to get the area of 16.
I hope this helped! If you need another example, feel free to ask!
:-)
Areas of quadrilaterals follow the formula A = bh, where b is the base and h is the height. What this formula means is you multiply the base length by the height length and you will have the area. The important thing to remember when calculating area is that the result will always be in units squared (example: 24 cm²). I'll do a few:
1) A = bh
A = 8(2)
A = 16 units²
(Since there is no unit given, just use the word units.)
2) A = 8(9)
A = 72
A = 72 units²
3) A = 6(5)
A = 30
A = 30 units²
I hope this helps you!
A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let w = quarts of water left in the tub and t = time in minutes.
Answers
Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then.
A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute.
Let w be the quarts of water left in the tub.
Let t be the time in minutes.
So, the equation to model this situation is :
Modelling equation: [tex]w=50-2.5t[/tex]
This equation is viable only up to when t is 20 minutes. That will give w = 0. More than 20 minutes is not possible.
Please help me !! Thank you!!
Answers
2. yes. The cost is proportional to the number of tickets, hence a linear function of the number of tickets.
3. no. The population is modeled by an exponential function.
4. yes. Distance is proportional to time at a constant speed.
5. yes. (maybe) In the context of this question, "at a constant rate" is presumed to mean "by a constant amount". In that case, growth is linear.
If the rate expressed as a constant percentage (say, 3%) per year, then growth is exponential, not linear.
HOW ARE RESTRICTIONS AND DISCONTINUITIES CREATED IN RATIONAL EXPRESSIONS? HOW CAN THEY BE ACCOUNTED FOR GRAPHICALLY?
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Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.
In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.
Explanation:In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.
For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.
Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.
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