The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Here, we are given a circle with center D and equation as-
[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]
Comparing this to the general form of equation of a circle which is [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-
g = 1, f = -4 and c = 8
thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3
Now, since PT is a tangent to the circle, DP will e perpendicular to PT.
We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)
= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]
= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]
= [tex]\sqrt{25 +4 }[/tex]
=[tex]\sqrt{29}[/tex]
Thus, in triangle, PDT by using Pythagoras theorem, we will have-
[tex]PT^{2} + DT^{2} = PD^{2}[/tex]
since DT is the radius of the circle, DT = 3
⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]
[tex]PT^{2} + 9 = 29[/tex]
[tex]PT^{2} = 29 - 9[/tex]
[tex]PT^{2} = 20[/tex]
[tex]PT = \sqrt{20}[/tex]
Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.
Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]
so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)
Thus, the equation of the circle will be-
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
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what is perpendicular consider of?
Answer: straight line that makes the right angle (90 degrees) with the other
Step-by-step explanation: In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other
A computer password is required to be 7 characters long. How many passwords are possible if the password requires 2 lowercase letter(s) followed by 5 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
We will see that there are 19,656,000 different passwords that can be made with the given characters.
How many passwords are possible?We need to find the number of possible options for each character of the password.
The first character is a letter, so we have 26 options.
The second character is another letter, so we have 25 options (because we can't repeat).
Then we have 5 digits, for each digit we have 10 options (removing one for each subsequent one)
First digit: 10 options.Second digit: 9 options.Third digit: 8 options.Fourth digit: 7 options.Fifth digit: 6 optionsThe total number of passwords is given by the product between the numbers of options.
P = 26*25*10*9*8*7*6 = 19,656,000
There are 19,656,000 different passwords that can be made.
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Patrick lost his lunch money on the way to
school. If he can get thirteen of his friends
to each give him a quarter, he can buy a
school lunch. How much does a school
lunch cost?
$_
Answer:
$3.25
Step-by-step explanation:
Each quarter is 25¢
13 quarters will be worth 13 x 25 = 325¢
Since 1$ = 100¢
divide 325¢ by 100 to get amount in $
= 325/100 = $3.25
Annie is selling chocolate bars for school. The cost of 12 bars is $18.
A) What is the unit rate of 1 candy bar?
B)How many bars must Annie sell to make $75?
Answer:
A) $1.5
B)50 bars
Step-by-step explanation:
A) First find out how much money one bar costs: 18/12= 1.5
$1.5 is how much one costs
B) Now that you know how much one bar costs, divide 75 by 1.5 to determine how many bars you need to get to $75.
75/1.5=50
50 bars to get to $75
Answer:$1.50 per bar and she would have to sell 50 bars to get 75
Step-by-step explanation: brainliest please? i could really use it
Find the area of the triangle:
Answer:30
Step-by-step explanation:
Let sets A and B be defined as follows. A is the set of integers greater than -8 and less than -4.B={b,h,i,l,r,s}
A
Concept
The cardinality of a set is a measure of the "number of elements" of the set. For example, the set contains 3 elements, and therefore. has a cardinality of 3.
Set A is the set of integers greater than -8 and less than -4.
Therefore set A = {-7, -6, -5,}
-7 is greater than -8 and -5 is less than -4 from the number line.
Therefore, set A = { -7, -6, -5 }
B = {b, h, i, l. r, s }
Cardinalities of
n(A) = 3 n(B) = 6
B
[tex]\begin{gathered} -5\text{ }E\text{ A = true} \\ -12\text{ E A = false} \\ b\text{ E B = true} \\ t\text{ }\notin\text{ B = true} \end{gathered}[/tex]
Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
3 answers for this problem.
CORRECT ANSWERS ONLY!!!
Sentences to Algebraic EquationsTranslate the following sentence into equations and solve them.1. The quotient of a number and six is five. Find the number.
1. The quotient of a number and six is five.
he algebraic expression ifor the previous sentence is:
x/6 = 5
multiply by 6 to solve for x:
x = 5(6)
x = 30
. Eight decreased by twice a number is four.
- 2x = 4 subtract 8 both sides
-2x = 4 - 8
2x = -4 divide by -2 both sides
x = 2
3. Three less than the division of a number to seven is one.
3 - x/7 = 1 subtract 3 both sidesa
-x/7 = 1 - 3
x/7 = -2 multiply by -7 both sides
x = 2
4. Seven times the difference of 15 and a number equals - 56.
7(15 - x) = -56 a
7(15) - 7x = -56
105 - 7x = -56 subtract 105 both sides
-7x = -56 - 105
7x = -161 divide by -7 both sides
x = 23
select 3 statements one for Cosine one for Tangent and one for sine
From the unit circle, we can deduce the 3 correct statements.
1. The first correct sine statement is;
[tex]\sin 45=\frac{\sqrt[]{2}}{2}[/tex]2. The correct cosine statement is;
[tex]\cos 45=\frac{\sqrt[]{2}}{2}[/tex]3. The correct tangent statement is;
[tex]\tan 45=1[/tex]Here's a diagram to show why
Solve for c.
a(c+b) = d
Answer: C=D\A-B THAT IS THE ANSWER
Step-by-step explanation:
Write a function(x) that calculates the cost of learning the machine for x months
The question provides that an initial fee of $1000 and a monthly fee of $115 is paid.
Since the initial fee is a one-time payment and the monthly fee is a recurring payment, over x months, the fee that would have been paid is given o be:
[tex]C(x)=1000+115x[/tex]After 1 year, 12months would have passed. This means that we can scalculate the cost using x = 12 in the equation:
[tex]\begin{gathered} x=12 \\ \therefore \\ C(x)=1000+115(12)=1000+1380 \\ C(x)=2380 \end{gathered}[/tex]ANSERS
(a) The function is:
[tex]C(x)=1000+115x[/tex](b) At the end of one year, he would have paid $2,380.
A president of a company wants to know if his employees think he is doing a good job. Which descriptions represents a sample? Select all that apply.
the president of the company’s family and relatives
the 5,000 residents of the town
25% of the workers at the company
the 1,000 total employees of the company
50% of the retirees from the company
The sample can be 25% of the workers of the company and 50% of the retirees.
Sampling is the practice of selecting a small group of individuals (a statistical sample) from a statistical population in order to make an educated guess about the characteristics of the full population.
It is utilized in survey methodology, quality control, and statistics. The goal of statisticians is to obtain samples that are representative of the population being studied. Sampling provides insights and is more economical and expedient than assessing the entire population when it is not practicable to do so.Each sample provides a numerical value for one or more properties of certain objects or individuals, such as their size, location, color, or weight. Weights can be applied to the data in survey sampling, particularly in stratified sampling, to account for the sample design.Now of the given options sample can only be selected from the groups that directly affect the president of the company.
Therefore the options will be :
25% of the workers at the company
50% of the retirees from the company
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Please help with this
Explanation
Given the function
[tex]y=arctanx[/tex]The domain of the function is given as
[tex]-\inftyAnswer: Option 3I don’t know how to do these
The area, A, of the regular polygons found their side lengths, s and the length of their apothem, are;
4. A ≈ 2144.5 cm²
6. A = 12080 in²
8. A ≈ 1168.5 m²
What is a regular polygon?A regular polygon is a polygon that have sides of the same length and that the sides are symmetric about a common central point.
The area of a regular polygon is given by the formula;
[tex] \displaystyle{A = \frac{n \times s\times a}{2} }[/tex]
Therefore, we have;
4. The area of a regular pentagon is given by the formula;
[tex]\displaystyle{A = \frac{5 \times s\times a}{2} }[/tex]
Where;
a = 24.3 cm, s = 35.3 cm, we have;
[tex]\displaystyle{A = \frac{5 \times 35.3 \times 24.3}{2} \approx 2144.5}[/tex]
The area of the pentagon is therefore; A ≈ 2144.5 cm²6. The area of a regular octagon is given by the formula;
[tex]\displaystyle{A = \frac{8 \cdot s\cdot a}{2} }[/tex]
Where;
a = 60.4 in,
s = 50 in
Which gives;
[tex]\displaystyle{A = \frac{8 \times 50\times 60.4}{2} = 12080 }[/tex]
The area of the octagon is A = 12080 in²8. The area of a regular decagon is given by the formula;
[tex]\displaystyle{A = \frac{10 \times s\times a}{2} }[/tex]
Where;
a = 19 m
s = 12.3 m
Which gives;
[tex]\displaystyle{A = \frac{10 \times 12.3\times 19}{2} = 1168.5}[/tex]
The area of the octagon is, A = 1168.5 m²Learn more about calculations with respect to regular polygons here;
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The stemplot displays 26 students' scores on a 90-point
statistics test. The lowest possible passing grade on the test was a 54 out of 90. What percentage of students passed this test ?
A. 23%
B. 54%
C. 77%
D. 96%
Answer:
C. 77%
Step-by-step explanation:
20 out of 26 people passed so
20 divided by 26 equals 76.9 so 77 percent
To celebrate its grand opening, a store is giving every 8th customer a 50$ gift certificate and every 5th customer a 10$ gift certificate. Which customer will be the first to receive both?
Find the equation of the linear function represented by the table below in slope-intercept form.X1234y-3-7-11-15
Answer:
The equation of the linear function represented in the table is y = -4x + 1.
Explanation:
Since the values in the x-variable are consecutive, let's take a look at the y-values.
Let's determine the common difference of the y-values.
[tex]\begin{gathered} -15-(-11)=-4 \\ -11-(-7)=-4 \\ -7-(-3)=-4 \end{gathered}[/tex]As we can see, the common difference between the y-values is -4. Therefore, the slope of the equation is -4.
To determine the y-intercept, let's subtract -4 from -3 to determine the y-value at x = 0.
[tex]-3-(-4)=1[/tex]Hence, the y-intercept is 1.
Therefore, the equation is y = -4x + 1.
please help im not sure how this works
Answer:
b i nthink
Step-by-step explanation:
B. maybe?
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I don’t understand how to do this i need all the help i can get. thank you.
The sum of the angles on a straight line is 180 degrees. This means that
angle MJO + angle NJO = 180
From the information given,
angle MJO = 131
angle NJO = 15x + 4
Thus,
131 + 15x + 4 = 180
135 + 15x = 180
15x = 180 - 135 = 45
x = 45/15
x = 3
We would substitute x = 3 into angle NJO = 15x + 4
angle NJO = 15 * 3 + 4 = 45 + 4
angle NJO = 49
Write an equation of the line.
Vertical; through (-3,-5)
Equation of the vertical line passing through point (-3, -5) is given by x = -3.
As given in the question,
Line passes through the point (-3, -5)
It represents the x- coordinate is equal to -3
And y- coordinate is equal to -5.
Condition for the line is given as vertical line.
Vertical line represent the value of x- coordinate remain constant.
It represent x-intercept
x = -3
x-intercept represents the equation of the vertical line.
Therefore, equation of the vertical line passing through point (-3, -5) is given by x = -3.
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f a 10 percent reduction in price leads to a 20 percent increase in quantity demanded, the coefficient of elasticity of demand would be equal to _______
The coefficient of elasticity of demand would be equal to 2 .
The price elasticity of demand for a good determines how responsive the desired amount is to the price (PED).
When prices rise, demand declines for almost all products, but some products are more negatively impacted than others. When a price increases by 1% while all other factors remain constant, the price elasticity provides the percentage change in quantity required. If the elasticity is 2, a 1% increase in price results in a 2% drop in the amount sought. The effect of changes in other variables on the necessary quantity is measured by various elasticities.We know that the coefficient of elasticity of demand is given by
ED = Change in demand(percent) ÷ change in price (percent)
ED = 20% ÷ 10% = 2
Hence the coefficient of elasticity of demand would be equal to 2 .
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Consider the equation 6 – x = 3 – x. The picture shows the graphs of y = 6 – x and y = 3 – x. Which statement is true?
The two lines never intersect (are parallel lines) thus the equation:
6 - x = 3 - x
Has no solutions.
What can we say about the equation?
Here we have the equation:
6 - x = 3 - x
And (supposedly) a graph of the two lines:
y = 6 - x
y = 3 - x
Notice that the part on the linear equations that depens of x is equal to the ones in the equation above.
So basically we have a system of equations:
y = 6 - x
y = 3 - x
Because "y" is the same thing in both equations, we can rewrite:
6 - x = y = 3 - x
If we remove the part in the middle, we return to the original equation:
6 - x = 3 - x
Now, the solution of that equation is given by the point where the two graphs of the linear equations intersect, it will never happen, because both linear equations are parallel (have the same slope) which means that the equation:
6 - x = 3 - x
Has no solutions.
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Answer:
its smthing about no solutions. Just pick the answer that says no solution satifies it
Step-by-step explanation:
i got it right on imagine math :))) (i dont have the screen shot)
REDUCING RATIOS
1. 55:33
2. 1,000:100
3. 560:80
4. 20:340
Answer:
Step-by-step explanation:
1. 5:3
2. 10:1
3. 7:1
4. 1:17
TRUE OR FALSE?
The Transitive property on N states that: For any two natural numbers a and b, either a > b or a = b or b> a.
Answer:
False a=b
Step-by-step explanation:
cos 20-2 cos0=-1
Find all solutions of the equation in the interval [0,2pie).
The solutions for the trigonometric cosine equation are [0, 90,2pi].
What is trigonometric cosine function?
Trigonometric is one of the branch in mathematics which is used to study the relationship between the length and angles. Its angle is categorized into six form depending upon their sides.
To calculate the solution of the given equation in the interval of [0, 2 pi].
Therefore, the given equation in the form of the trigonometric function is as written below:
[tex]cos^{2} 0 - 2cos0 +1 = 0\\(cos0-1)^{2} =0[/tex]
Hence, the solutions for the trigonometric cosine equation are [0, 90,2pi].
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A factory produces sweatshirts for a sports team, and packages the sweatshirts in boxes of 20. Every
hour, the factory produces 9,284 sweatshirts.
How many full boxes of sweatshirts are packaged in 1 hour?
Answer:
464 remainder 2
Step-by-step explanation:
9284÷20
The change in the value of a stock is represented by the rational number -6.50 describe in words what this means
The rational number given in words mean that the value of the stock has declined or decreased by 6.50.
What is a negative number?A rational number is a number that can be expressed as a fraction of two integers. Rational numbers can be positive or negative.
A negative number is a number that is smaller than zero. A negative number usually has this sign, -, preceding it. An example of a negative number is -6.50.
When a stock's value is represented by a negative number, it means that the value of the stock has declined or fallen.
On the other hand, if the stock's value is represented by a positive number, it means that the value of the stock has increased.
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Noah has collected $50 by selling lemonade and muffins. He sold $10 worth of muffins. He sold each cup of
lemonade for $2. How many cups of lemonade did he sell?
Choose the correct equation.
a. 2x-10-50
b. 2x+10=50
c. 2x+50=10
d. 10x+2=50
13. Highlight the answer choice that represents the distance between the two points below. Round to the nearest hundredth if necessary. You may use a calculator.
A. 10
B. 28
C. 3100
D. 10
E. 310
F. 3.16
Supposing that the two points are (2,4) and (10,10), the distance between them is given by:
A. 10.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:
[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]
Hence the distance is of 10 units and option A is correct.
What is the missing information?This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).
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Send the answer's please.
Answer:
A 573308928
B. 124176266400000000000000000