The value of x in the series given the first three terms x + 5, x + 1 and x is 1/3
Given that, we have
x + 5, x + 1 and x
Using the common ratio, we have
(x + 5)/(x + 1) = (x + 1)/x
So, we have
x² + 5x = x² + 2x + 1
Evaluating the like terms, we have
3x = 1
Divide by 3
x = 1/3
Hence, the value of x is 1/3
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The first used 20 gal of fuel and the second used 25 gal. The 2 drove 1450 miles and the sum of their fuel efficiencies was 65 miles per gal. What we’re each car fuel efficiency?
Answer: there you go :)
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Question 1
Write an equation for the surface area of a prism with a length, width, and height of x
inches.
Answer:
The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Since the length, width, and height of the prism in this case are all x inches, we can substitute x for l, w, and h in the formula to get:
Surface Area = 2(x)(x) + 2(x)(x) + 2(x)(x)
Simplifying the equation, we get:
Surface Area = 2x^2 + 2x^2 + 2x^2
Surface Area = 6x^2
Therefore, the equation for the surface area of a prism with a length, width, and height of x inches is:
Surface Area = 6x^2 square inches
pls help with this question im offering all of my tokens for this
Answer:
34 ft.²
Step-by-step explanation:
We can find the area of this polygon by splitting it into two rectangles.
We can find the area of each individual rectangle, then add their areas to get the area of the entire polygon.
See the attached image for a diagram.
First, we can find the area of the smaller rectangle.
length × width
5 ft. × 2 ft. = 10 ft.²
Next, we can find the area of the larger rectangle.
4 ft. × 6 ft. = 24 ft.²
Finally, we can add the two rectangles' areas together to get the area of the entire polygon.
10 ft.² + 24 ft.² = 34 ft.²
The diameter of a cone's circular base is 6 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
Answer:
The correct answer is 36π
Step-by-step explanation:
A die is rolled 2 times. What is the probability of getting a 1 on the first roll and a 2 on the second roll.
The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is [tex]\frac{1}{18}[/tex] .
What about probability?
In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.
For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.
According to the given information:
When a die is rolled 2 times, the output we get
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Total no of getting '1' on first roll and '2' on second roll = 2
Total outcomes = 36
⇒ [tex]\frac{2}{36}[/tex]
⇒ [tex]\frac{1}{18}[/tex]
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As an experiment, a charity decides to use SMART to determine a shortlist from the seven applicants who have
applied for the post of Regional Officer for the Western Region. The main criteria which will be used to
compare candidates are: salary they would expect (SALARY), their experience of charity work (CHARITY EXP),
their managerial experience (MANAGEMENT EXP), their educational qualifications (EDUCATION), their
apparent commitment to the charity's work (COMMITMENT) and the quality of the ideas they put forward on
the form (IDEAS).
(a) Discuss if the weights of the attributes are appropriate. If so, why do you think so? If not, why do you
think the weights are not appropriate? (You don't need to discuss whether the attributes are
appropriate. Only focus on the "weights". This is your own opinion and subjective. You don't need
references for this.)
The personnel manager ranked all the criteria, except salary, in order of importance and then assigned weights
as follows:
COMMITMENT
MANAGEMENT EXP
IDEAS
CHARITY EXP
EDUCATION
Candidate A's aggregated score is 50.
(You don't need to worry about how 50 was calculated.)
The other candidates' aggregated scores are found below.
100
70
65
55
10
b) Scatter plot chart would indicate a positive correlation
c) Candidate D would be the most cost-effective choice, as their expected salary would increase the most. Candidate F would also be a good choice, as their expected salary would increase by £1,000.
What is a Scatter plot chart?A scatter plot chart can be used to plot the data of the two variables on a two-dimensional graph, and the data points can be connected with a line or a curve.
a) The weights of the attributes in this case seem to be appropriate for the purpose of selecting a Regional Officer for the Western Region.
This data shows that the charity is placing a greater emphasis on the candidate's commitment, managerial experience and ideas, as these are likely to be the most important factors in selecting a successful Regional Officer.
Additionally, Education has the lowest weight at 10, indicating that this is not a major factor in consideration.
Overall, the weight of each criteria reflects the importance of the criteria to the charity and is appropriate for this case.
b) The scatter plot chart would indicate a positive correlation between the two variables, with the higher aggregate score corresponding to the higher expected salary.
Based on this chart, candidates A, D and F would be the best 2-3 candidates, with the highest aggregate scores of 50, 90 and 62 respectively.
c) If the charity is prepared to pay £1,000 for each additional aggregate score, then candidate D would be the most cost-effective choice, as their expected salary would increase the most (from £60,000 to £61,000). Candidate F would also be a good choice, as their expected salary would increase by £1,000 (from £52,000 to £53,000).
Candidate A would not be recommended, as their expected salary would increase by only £500 (from £46,000 to £46,500).
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A company performs $3,200 of services during the month and bills customers. The customers are expected to pay next month.
Record the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting.
Recording the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting is as follows:
a) Accrual Method:Customer Billing:
Debit Accounts Receivable $3,200
Credit Service Revenue $3,200
(To record the performance of services for customers during the month.)
b) Cash Method:Customer Billing:
No Record during the current month.
What differentiates cash-basis accounting from accrual-basis accounting?Cash-basis accounting recognizes expenses and revenues when cash exchange takes place.
Accrual-basis accounting matches expenses and revenues to the month or period when the transaction occurs, whether there is a cash exchange or not.
For instance, the accrual-basis will recognize the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Accounts Receivable $3,200
On the other hand, the cash-basis will recognize revenue with the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Service Revenue $3,200
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Consider a random variable X with PDF
fX(x) = (2x/3, if 1 < x ≤ 2,
0, otherwise,
and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
By answering the presented question, we may conclude that As a result, variable P(A) = 0.667.
What is a Variable?A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values. These include things like size, age, money, where you were born, academic status, and your kind of dwelling, to name a few. Variables may be divided into two main categories using both numerical and categorical methods.
To compute E[X], we must integrate the PDF X times over its support:
From x=1 to x=2, E[X] = x fX(x) dx
Because the PDF is only non-zero in the interval (1,2), we have:
[tex]E[X] = x(2x/3) dx between x=1.5 and x=2.E[X] = (2/3) x2 dx between x=1.5 and x=2.E[X] = (2/3) [(2^3)/3 - (1.5)^3]E[X] = (2/3) [8/3 - (27/8)]E[X] = 19/12As a result, E[X] = 1.583.[/tex]
P(A) is calculated by integrating the PDF across the area where X is higher than or equal to 1.5:
[tex]P(A) = fX(x) dx between x=1.5 and x=2.P(A) = (2x/3) dx between x=1.5 and x=2.P(A) = [(2/3)x^2] between x=1.5 and x=2P(A) = (2/3)(2^2 - 1.5^2)P(A) = 2/3As a result, P(A) = 0.667.[/tex]
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Complete question -
Consider a random variable X with PDF fX(x) = (2x/3, if 1 < x ≤ 2, 0, otherwise, and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].
The table summarizes results from 982 pedestrian deaths that were caused by automobile accidents.
Zacharias wants to download some songs
through an app on his phone. Each song
costs $2 to download and he has $12
remaining in his account. The inequality
2s < 12 represents the number of songs s
he could download. What is the greatest
number of songs Zacharias can download?
Answer: 6 songs.
Step-by-step explanation:
Each song is $2 dollars. $12 divided by $2 equals 6.
So he can download 6 songs.
11.) Mr. Moran is packing orders for his candle business. One customer ordered 14
vanilla-scented candles. If each candle weighs 12 ounces, how many pounds does
this order weigh?
Answer : 10.5
Explanation: Divide 168/16
Ethan sold 2/3 gallons of lemonade.Kayla sold some lemonade too.Together,they sold 1 1/4 gallons.
Who sold more lemonade,Ethan or Kayla? How much more
Answer: Kayla sold 1/12 gallons more than Ethan.
Step-by-step explanation:
Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:
Kayla's sales = Total sales - Ethan's sales
Kayla's sales = 5/4 - 2/3
To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:
Kayla's sales = (5/4)(3/3) - (2/3)(4/4)
Kayla's sales = 15/12 - 8/12
Kayla's sales = 7/12
Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:
Ethan's sales = (2/3)(4/4) = 8/12
Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:
Kayla's sales - Ethan's sales = 7/12 - 8/12
Kayla's sales - Ethan's sales = -1/12
The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.
Find the volume of the figure.
Answer:
165inch^3
Step-by-step explanation:
4×7×3=84inch^3
9×3×3=81inch^3
84+81=165inch^3
Which of the following describes the absolute value of a number?
The absolute value of a number is the square root of the
number.
The absolute value of a number is the negative value of the
number.
The absolute value of a number is the square root of the
positive value of the number.
The absolute value of a number is the positive value of the
number.
The absolute value of a number is its negative recicprocal.
Answer: Your answer should be
D
Step-by-step explanation: this is because absolute value makes a number positive, no matter the scenario as long as the number(s) are in the absolute value sign (indicated basically by straight lines) this makes it to where the number can never be negative within the lines.
How to solve “What is m
Answer: 120
Step-by-step explanation:
The angle measures should add up to 360
110+130+x=360
240+x=360
x=120
Trigonometry: Sum and difference Identities
MUST GIVE EXPLANATION:
Will give BRAINLIEST.
Using the sum-to-product formula we get the value as √2 cos(2α)
What is the sum-to-product formula?
The sum-to-product formula is a trigonometric identity that expresses the sum or difference of two trigonometric functions as a product of two trigonometric functions. There are several versions of this formula, depending on the specific functions involved.
We can use the sum-to-product formula to simplify the expression:
cos(2α - π/16) + cos(9π/16 - 2α)
= cos(2α)cos(π/16) - sin(2α)sin(π/16) + cos(9π/16)cos(2α) + sin(9π/16)sin(2α)
= cos(2α)(cos(π/16) + cos(9π/16)) + sin(2α)(-sin(π/16) + sin(9π/16))
= cos(2α)(2cos(5π/16)cos(3π/16)) - sin(2α)(2cos(7π/16)sin(π/16)) (using the sum-to-product formula again)
= 2cos(2α)cos(5π/16)cos(3π/16) - 2sin(2α)cos(7π/16)sin(π/16)
= 2cos(2α)(cos(5π/16)cos(3π/16) - sin(5π/16)sin(3π/16)) (using the product-to-sum formula)
= 2cos(2α)cos(π/4)
= 2cos(2α)/√2
= √2 cos(2α)
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the table shows the heights and masses of a male gorrila and a female gorilla at zoo.Based on the table, wich statement is true?
Using mensuration, we can find that the mass of male is greater than that of the female's by 63.507kg.
Define mensuration?Mensuration can be defined as a measurement action. Our world is three dimensional. Both elementary school mathematics and secondary school mathematics heavily rely on the idea of measurement. Also, measuring is directly related to our daily life. When we learn to measure items, we practise measuring both 2D and 3D shapes. Both conventional and nonconventional units of measurement can be used to determine the size of objects or quantities.
In the given table,
Height of male = 1.68m.
Mass of male = 158.757kg.
Height of female = 1.448m.
Mass of female = 95.25kg.
Difference between mass of male and female,
= 158.757 - 95.25
= 63.507kg.
The mass of male is greater than that of the female's by 63.507kg.
So, 2nd statement is true.
Rest of the statements are not true.
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"A number decreased cubed by 24"
The expression that represents the sentence "A number cubed decreased by 24" is given as follows:
x³ - 24.
What is the algebraic expression that models the sentence?The sentence for this problem is defined as follows:
"A number cubed decreased by 24".
The number is unknown, hence the variable that represents the number is given as follows:
x.
The cube of the number is given as follows:
x³.
The number is then decreased by 24, hence we subtract the expression x³ by 24 to obtain the algebraic expression as follows:
x³ - 24.
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Helpppp pleaseee
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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PLEASE HELP!!! i am failing and im going to be held back if i dont get my grade up!!!!
Emma spent $45.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels.
5d + 5.25 = 45.2
What was the price of each dozen of bagels?
A.
$6.99
B.
$7.99
C.
$9.04
D.
$3.79
Answer:
the answer to the question is B
Step-by-step explanation:
no need for explanation just trust the source
PLEASE HELP FAST!!
Solve the following system by elimination. CHECK the solution.
- 3x - 6y = - 27
4x - 2y= -4
Answer: -3x - 6y = -27 (Equation 1)
4x - 2y = -4 (Equation 2)
We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.
In this case, we can start by multiplying Equation 2 by 3 to eliminate the y variable:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
Now we can add Equation 1 to Equation 2:
-3x - 6y = -27 (Equation 1)
12x - 6y = -12 (Equation 2 multiplied by 3)
9x = -39
Simplifying this expression, we get:
x = -39/9 = -13/3
Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
-3x - 6y = -27
-3(-13/3) - 6y = -27
13 + 6y = -27
6y = -40
y = -40/6 = -20/3
Therefore, the solution to the system of equations is x = -13/3 and y = -20/3, or (-13/3, -20/3) in coordinate form.
To check the solution, we can substitute the values of x and y into both equations:
-3(-13/3) - 6(-20/3) = -27
4(-13/3) - 2(-20/3) = -4
Simplifying both expressions, we get:
13 + 40 = 27 (which is true)
-52/3 + 40/3 = -4 (which is also true)
Therefore, the solution is correct.
Step-by-step explanation:
what month comes under the 250th day of the year?
Answer:september
Step-by-step explanation:
log19(53.875) to base 10
Log base 19 of 53.875 is approximately 0.97212 when converted to base 10.
To convert log base 19 of 53.875 to base 10, we can use the formula:
log base b of x = log base a of x / log base a of b
where a: current base and b: desired base.
So, in this case, we want to convert log base 19 of 53.875 to base 10. We can use the formula above with a = 19 and b = 10:
[tex]log base 10 of 53.875 = log base 19 of 53.875 / log base 19 of 10[/tex]
Log base 19 of 10 is equal to 1/log base 10 of 19, since the logarithm of 10 to any base is equal to 1. Using a calculator, we can determine that the log base 10 of 19 is roughly 1.278753.
Substituting:
log base 10 of 53.875 = log base 19 of 53.875 / 1.278753
To find the value of log base 19 of 53.875, we can use a calculator to evaluate log base 19 of 53.875, which is approximately 1.244036.
Substitute to equation:
log base 10 of 53.875 = 1.244036 / 1.278753
Simplify to get:
log base 10 of 53.875 = 0.97212
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The following images are some basic limits on graphs , please answer them.
The piecewise function formed by two functions and a point is not continuous at x = 1.
How to determine limits in a piecewise function
In this problem we find the case of a piecewise function formed by three expressions in three corresponding intervals: two functions and a point. These expressions are defined in the images attached below. The x-value is on the horizontal axis and the y-value is on the vertical axis.
According to the first figure, the y-value of the function is getting closer to 2 as x approaches 1 from the left side.
According to the second figure, the y-value of the function is getting closer to 3 as x approaches 1 from the left side.
According to the third figure, the y-value of the function is equal to 0.5 when x is equal to 1.
Therefore, the piecewise function is not continuous at x = 1.
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A survey of all beings on planet Boondin found that 60% preferred hopt
juice to all other juices. If 50 beings were surveyed altogether, how
many of them preferred hopt juice?
label optional
Answer:
If 60% of the beings surveyed preferred hopt juice and 50 beings were surveyed altogether, then we can calculate the number of beings who preferred hopt juice by multiplying the total number of beings surveyed by the percentage that preferred hopt juice: `50 x 0.60 = 30`. So, **30** beings preferred hopt juice.
Help me please!!!!!!
Due to its neighbouring perpendicular sides and opposite parallel and equal-length sides, the quadrilateral ABCD is a rectangle.
What are the properties of parallelogram?a) The opposite sides are parallel and equal.
b) The opposite angles are equal.
c) The consecutive or adjacent angles are supplementary.
d) If any one of the angles is a right angle, then all the other angles will be at right angle.
e) The two diagonals bisect each other.
4. To find the area of a parallelogram, you can follow these steps:
Measure the length of the base of the parallelogram. Let's call this measurement "b".
Measure the height of the parallelogram. Let's call this measurement "h".
Multiply the base length "b" by the height "h" to get the area of the parallelogram.
Therefore, the formula to calculate the area of a parallelogram is:
Area = base length (b) [tex]*[/tex] height (h)
In symbols, this can be written as:
[tex]A = b \times h[/tex]
Alternatively, if the length of both adjacent sides is known, you can use the formula:
A = base length (b) [tex]*[/tex] the length of adjacent [tex]side (a) * sin[/tex](θ)
where theta is the angle between the base and adjacent side.
5. the given vertices on a coordinate plane and see what kind of figure they form.
The figure formed by the vertices A, B, C, and D is a quadrilateral. To determine the precise classification of the quadrilateral, we can use its properties.
To determine if the parallelogram is a rhombus, rectangle, or square, we need to check if the diagonals bisect each other and if the adjacent sides are perpendicular. We can find the midpoint of AC and BD as:
Midpoint of AC: [tex]((2 + 8)/2, (3 + 7)/2) = (5, 5)[/tex]
Midpoint of BD: [tex]((7 + 3)/2, (2 + 8)/2) = (5, 5)[/tex]
The diagonals AC and BD intersect at the midpoint [tex](5,5)[/tex], so they bisect each other.
We can also find the slopes of adjacent sides AB and BC, and we find that they are:
AB: [tex]-1/5[/tex]
BC: [tex]5[/tex]
The product of their slopes is [tex]-1[/tex], so the adjacent sides are perpendicular.
Therefore, the quadrilateral ABCD is a rectangle, because it has opposite sides that are parallel and equal in length, and adjacent sides that are perpendicular.
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Each time Caroline goes shopping she decides whether or not to buy fruit. The probability that she does buy fruit is 0.4. Independently, she then decides whether or not to buy a CD, with a probability of 0.6 that she does buy a CD. Work out the probability that she buys fruit or buys a CD or both.
Answer:
To work out the probability that Caroline buys fruit or buys a CD or both, you can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are events.
In this case, A is the event that Caroline buys fruit and B is the event that Caroline buys a CD.
The probability that Caroline buys fruit is 0.4 and the probability that Caroline buys a CD is 0.6.
To find the probability that Caroline buys fruit and a CD, you can multiply the probabilities of the two events:
P(A and B) = P(A) x P(B) = 0.4 x 0.6 = 0.24
Therefore, the probability that Caroline buys fruit or buys a CD or both is:
P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.6 - 0.24 = 0.76
So, the probability that Caroline buys fruit or buys a CD or both is 0.76 .
Please I’d love some help with a simple explanation on how you got the answers and the answers (obviously)
Given the above circles,
1) x = 42°
2) x = 29°
3) x = 101°
4) x = 37°
5) x = 31°
6) x = 120°
What is the explanation for the above results?1) x = 42° because the Angles at the circumference of a circle
subtended by the same arc are equal. Since 35° and 103° are two of the three angles in a triangle whose third angle subtends the circumference of the circle along with ∠x, and the third angle = 180 - 35 - 103 = 42° therefore, x = 42°
2) x = 29° because according to the central angle theorem, the angle at the circumference is double the one at the center. Since the angle at the circumference is 61°, the one at the center is 122°. Since the line from the center that couches on both sides of the circumference is the radius, they are equal. Hence, the angles formed at their bases are equal.
Thus, x = (180-122)/2
x = 29°
3) 3) x = 101° because the opposite angles of a cyclic quadrilateral are supplementary.
4) x = 37° based on the angle in the alternate segment theorem.
5) x= 31° is based on the "inscribed angle theorem" or the "theorem of the intercepted arc".
This theorem states that if an angle is inscribed in a semicircle, then the angle is a right angle (i.e., it measures 90 degrees). In other words, if you draw any two chords from the ends of the diameter to any point on the arc of the semicircle, then the angle formed by these two chords at the point on the arc will always be 90 degrees.
6) x = 120° on the basis of the "Tangent-Secant Angle Theorem" or "Tangent-Chord Angle Theorem".
In the problem given above, the angle x is formed by two tangents intersecting at the vertex outside the circle, and the Tangent-Secant (or Tangent-Chord) Angle Theorem is used to find its measure.
The arc formed at the points where the two tangents meet is twice the angle formed inside the circle which is = 30°
Thus, where the rest of the arc traced from the upper point of tangency is traced back to the lower point of tangency is called A,
The measure of arc A is 360° - 60° = 300°.
The measure of angle x is half the difference between the measures of the intercepted arcs, which is (300° - 60°)/2 = 120°.
Therefore, the measure of angle x would be 120°.
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A parabola opening up or down has vertex
(-4, -6) and passes through (-14, 13/2)
Write its equation in vertex form.
Answer:
To write the equation of the parabola in vertex form, we use the standard form:
y = a(x - h)^2 + k, where (h, k) is the vertex.
Given that the vertex is (-4, -6), we have:
h = -4 and k = -6
Now, we need to find the value of "a" using the point (-14, 13/2) which lies on the parabola.
Substituting the values in the standard form, we get:
13/2 = a(-14 - (-4))^2 - 6
Simplifying, we get:
13/2 = 100a - 6
100a = 13/2 + 6
a = 19/200
Therefore, the equation of the parabola in vertex form is:
y = (19/200)(x + 4)^2 - 6
Step-by-step explanation:
Plot 1 7/8 abd 2 1/2 on the number line