Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:
y+3=-1/2(x-2)
We can simplify this to
y= -1/2x-2
We can then check the point of intersection:
-1/2x-2=2x+3
-5=2.5x
x=-2
we can plug this in to the first equation to get y=2(-2)+3=-1
So the point of intersection of the circle and the tangent line is (-2,-1)
Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.
[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]
The radius of the circle is [tex]2\sqrt{5}[/tex]
For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The line y=2x+3 is tangent to the circle with center (2,-3)
The distance from the center of the circle to the line is equal to the radius of the circle.
The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:
d = |Ax₁+ By₁ + C| /√A² + B²
The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.
d = |-2(2) + (-3) - 3| / √(-2)² + 1²
d=10/√5
The radius of the circle is equal to the distance from the center to the tangent line, which is:
radius = 10/√5
Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
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A store clerk sold 25 Mathematics books and 10 English books for a total of $855. If she had sold 10 Mathematics books and 40 English books, she would have got $135 more. form a pair of linear equations and calculate the price of each book.
Answer:
855+135=990
90x11=990
10x11=110
25x11=275
110+275=385 990+110=1100
385+1100=1485
1485/11=135
the math books was $11 each so all to gether it is $275.
the english books was $65 each so all to gether it is 715.
275+715=990
Step-by-step explanation:
The required price of a Mathematics book is $27 and the price of an English book is $18.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's assume that the price of a Mathematics book is x dollars and the price of an English book is y dollars. Then we can form two equations based on the given information:
Equation 1: 25x + 10y = 855
This equation represents the total amount earned by selling 25 Mathematics books and 10 English books for $855.
Equation 2: 10x + 40y = 990
This equation represents the total amount that would have been earned by selling 10 Mathematics books and 40 English books for $135 more than the original total.
To solve for x and y, we can use elimination or substitution. Let's use elimination:
Multiplying Equation 1 by 4, we get:
100x + 40y = 3420
Now, we can subtract Equation 2 from this equation to eliminate y:
90x = 2430
x = 27
Substituting x = 27 into Equation 1, we can solve for y:
25(27) + 10y = 855
675 + 10y = 855
10y = 180
y = 18
Therefore, the price of a Mathematics book is $27 and the price of an English book is $18.
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Exercise on Properties/Laws of Sets Simplify each of the following identities to its simplest form, using the laws of sets; (i) (An B) U (AU B')'
(ii) An (AUB)
(iii) (CUA N (BUA)
1. The total amount of what you eam during the pay period before taxes and deductions are taken out is known as what?
Wage
Net pay
Salary
Gross pay
Answer:
net pay if im not mistaking
Step-by-step explanation:
Put these fractions in order from least to greatest:
Answer:
1/4, 3/8, 2/3
Step-by-step explanation:
3/8 is more than 25% (1/4) but is less than 66% (2/3) making the order 1/4 3/8 2/3.
Answer:
The answer is the 3rd option. (1/4, 3/8, 2/3)
Step-by-step explanation:
All u have to do is find a common denominator for all 3 fractions.
The common denominator in this problem would be 24
So lets convert all the fractions with a denominator of 24.
1/4 = 6/24
3/8 = 9/24
2/3 = 16/24
Since we now converted the fractions with a common denominator, we can deduce the order from least to greatest.
6/24, 9/24, then 16/24
In other words, the answer is the 3rd option. (1/4, 2/8, and 2/4)
Hope this helps! :0
૮ ・ﻌ・ა
Which of the segments below is a secant?
С
F
О.
В
Д.
А
u
А. ОВ
B. AB
ООО О
C. DE
D. AD
Answer:
it is d i believe
The secant of a circle is line segment AD. Therefore, option C is the correct answer.
What is secant of a circle?A line that crosses a circle at two different locations is said to be a secant of the circle. The Roman verb secare, which meaning to cut, is the source of the word secant. It can also be thought of as the chord of a circle extended outside of the circle.
Given that, circle with center O.
In the given figure, FC is chord, OB is radius, AB is tangent, AD is secant and DE is tangent.
Therefore, option C is the correct answer.
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Planes A and B are shown.
If a new line, p, is drawn parallel to line I, which
statement is true?
ZA
O Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line 1
O Line p must be drawn in the same plane as line n.
m
Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What is the price of one chair? Use the drop-down menus to complete parts A and B below.
The price of one chair Ben bought is $80 and he bought 6 chairs in total.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.
Assuming each chair costs $x and his total cost is $720.
∴ 240 + 6x = 720.
6x = 720 - 240.
6x = 480.
x = 80
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A TON OF POINTS AND BRAINLIEST IF ANSWERED CORRECTLY! I RLY NEED HELP PLZZZ ANSWER
Use the function f(x) = 2x^2 − 3x − 5 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Answer:
Step-by-step explanation:
For
f(x) = 2x2-3x -5
For Part A
Set f(x) = 0
Factor the Quadratic
Set the factors = 0
Solve each factor for x to find your x intercepts
For Part B
You need to use the coefficients in your Quadratic
List them
a = 2 , b = -3 and c = -5
Since a is positive, your parabola opens up
Find the x coordinate of the vertex it is -b/2a
One you get the x coordinate, plug it into to your Quadratic to get f(x) your y coordinate of the vertex
For Part C
You can plot the vertex, both x intercepts on a coordinate grid
If Justin raves his Chevy Camaro south down 1-540 for 2560 meters in 60 seconds, what is his velocity?
Henry jumped up 6 steps. Each step was 3/10 feet high. How high did he jump all together (in simplest form)
Answer:
1.8 or 14/5
Step-by-step explanation:
HENry MuST Be A KaNGaRoO
Answer:
Step-by-step explanation:
Multiply "3/10 ft high per step" by "6 steps." This works out to:
18/10 ft was the highest that this young man jumped.
This reduces to 9/5 ft, or 1.8 ft
Help (≧∇≦)b only question 15
Answer: 6 minutes 47.30 seconds is more faster by 4.71 seconds :D
Step-by-step explanation:
in - order to find out the answer, you must subtract ! why ? because in racing events the lowest time is the fastest !
Equation : 6 minutes 52.01 seconds - 6 minutes 47.30 seconds
Answer : 4.71 seconds
good luck on your homework ( also is that a savvas realize book ? 0-0 ) !!
of the negative number, and of the
16
6 The sum of a negative number,
negative number is – 13.2. What is the negative number?
Answer:
semoga jawabannya benar
Step-by-step explanation:
Korelasi Rank Spearman digunakan untuk mencari hubungan atau untuk menguji signifikansi hipotesis asosiatif bila masing-masing variabel yang dihubungkan berbentuk Ordinal.
Answer:
179.2
Step-by-step explanation:
166 = x + -13.2
166 - -13.2 = 166 + 13.2 = 179.2
PLEASE HELP ME
Question 7 of 10
Which of the following is equal to the fraction below? (5/9)⁸
A. 5⁸/9⁸
B. 5/9⁸
c. 5⁸/9
D. 8•(5/9)
SUBMIT
Answer:
A 5⁸/9⁸
Step-by-step explanation:
the bracket there shows that the power is for both the numerator and denominator so A is the correct answer
At the same time of day, a woman who is 78 inches tall casts a 63-inch shadow and her son casts a 21-inch shadow. What is the son's height? *
Answer:
26in
Step-by-step explanation:
The heights of the people in relation to their shadow lengths are proportional.
78in/63in = x/21in
The child's shadow is 1/3 the length of his mom so his height is 1/3 of hers.
78/3 = 26 in
Answer:
The son is 26 inches tall.
Step-by-step explanation:
[tex]\frac{x}{21} = \frac{78}{63}[/tex]
[tex]x= \frac{21x78}{63}[/tex]
21x78= 1638
1638÷63=26
Hope this helps
Sorry if I got it wrong!
Name the triangle described
Answer:
acute angle
Step-by-step explanation:
different angles will produce different "opposite side" lenghts, so the angle has 3 distinct angles and therefore 3 distinct sides, different sides means is an Scalene.
Now, one of the angles is 90° or namely a right-angle, that makes it a Right Scalene Triangle.
In Exercises 12-20, TA=AB=BC and TD= DE = EF
Write an Equation that relates AD and BE.
Based on the midsegment theorem of a triangle, the equation that relates AD and BE is: AD = ½(BE)
Recall:
The midsegment theorem of a triangle states that length of midsegment = ½(the third side of the triangle).Given the image attached below, where, TA=AB=BC and TD= DE = EF, considering ΔTBE:
AD = midsegment of ΔTBEBE = third side of ΔTBETherefore, based on the midsegment theorem of a triangle, the equation that relates AD and BE is: AD = ½(BE)
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6.
In a decorative figurine shop, it takes of an hour to paint 8
identical ceramic figurines. How long does it take to paint one
figurine? At the same rate, how long would it take to paint 12
figurines?
The time it would take to paint one figurine is 0.125 hour.
The time it would take to paint 8 figurine is 1.5 hours.
The first step is to determine the average rate. Average rate is the total ceramic figurines painted divided by the total time.
Average rate = 8 /1 = 8 figurines / hour
In order to determine how long it would take to paint 8 figurines, divide 12 by the average rate.
1 / 8 = 0.125 hour
In order to determine how long it would take to paint 8 figurines, divide 12 by the average rate.
12 / 8 = 1.5 hours
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2
Which function has a greater rate of change?
Function 1
Function 2
4
3
2
The function whose input x and
output y are related by
1
X+
2
-*x+7
14-3-2-1 1 2 3 4
2
A) Function 1
B) Function 2
C) Neither, they are equal
D) Neither, one is nonlinear
Given
f(x) = 3x^2+ 2x – 1 and g(x) =4x- 5find (gof)(-2)
Answer:
27
Step-by-step explanation:
yeah-ya......... right?
13,22,31,...
Find the 31st term.
Find the 31st term.
Answer: 283
Step-by-step explanation:
To do this, it is helpful to get an equation you can use to solve any term.
This equation is:
[tex]13 + 9(n-1)[/tex]
So simply plug in 31 for n to get
[tex]13+9(31-1)[/tex]
[tex]=13+270[/tex]
[tex]=283[/tex]
Answer:
283
Step-by-step explanation:
9x+4=9(31)+4=283
13+9=22
22+9=31
9x
9(1)=9 9+4=13
9x+4
You need to buy bananas at the store, but you realize you only have $2. How many bananas could you buy if they each cost 30 cents?
Answer:
6 bananas
Step-by-step explanation:
2 ÷ 0.30 = 6.6 repeating so 6 bananas
EC
What is the Arabic numeral for this Roman numeral?
VII
07
09
08
STUR
Answer:
07
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
V = 5
I = 1
V + I + I = 5 + 1 + 1 = 7
Hope that helps
The first term of an AP is p & it's common difference is q. What it's 10th term?
The first term of an AP = p
The common difference = q
We know that
nth term of an AP = a+(n-1)d
10th term = a+(10-1)d = a+9d
t10 = p+9q
Tenth term of the AP is p+9q
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If the 17th term of an AP exceeds the 10th term by 7, then the common difference is_____
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The distance between a 16 foot tall flagpole and a 40 foot tall tree is equal to the sum of the lengths of their shadows. If the flagpole casts a 18 foot shadow, find the distance from the flagpole to the tree.
Answer:
The distance from the flagpole to the tree is 27 ft
Step-by-step explanation:
Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3.
The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
Geometric progression is given by:
[tex]nth\ term=ar^{n-1}[/tex]
where a is the first term, r is the common ratio
Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3
[tex]First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486[/tex]
The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
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Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
Step-by-step explanation:
a² + b² = c²
12² + b² = 15²
b² = 225 - 144
b² = 81
b = 9
The ratio of the sides of two similar regular octagons is 5:7. If the measure of each side of the larger octagon is 21 cm, then the measure of each side of the smaller octagon is ________cm.
Answer:
15 centimeters.
Step-by-step explanation:
If the ratio of two sides of similar octagons is 5:7, then the larger octagon has a side length that is 7/5 times the smaller one. If the measure of the side of the larger octagon is 21, then the measure of the smaller one is 5/7 times that, which is 5/7 * 21 = 15 centimeters.
Which of the following correctly shows the quotient of 75 divided by 5
Answer:
answer is when u will multiply 5 with 15 then u will got your answer
just kidding answer is 75
so 75 is quotient
but have written which of the following ( in the question)
so where is the options .write an expression that shows 9 less than the product of 11 and 3.5
try this for answer (11×3.5)-9=x
2a+b+c=9 a+2b+c=8 a+b+2c=11
[tex] \: \: \: \: \: \: [/tex]
# 2a+b+c=9answer
[tex]a = \frac{9}{2} - \frac{1}{2} b - \frac{1}{2} c[/tex]
#a+2b+c=8answer
[tex]a = 8 - 2b - c[/tex]
#a+b+2c=11answer
[tex]a = 11 - b - 2c[/tex]
refer to the attachment for explanationhope it helps