Answers
Answer:
9
Step-by-step explanation:
Because line PQ and line PR are both tangent to circle S, it would result in them being equal. So first to find PQ, you would have to find the value of variable x. To do this you would set both equations equal to each other and solve
6x - 9 = 2x + 3
-2x -2x
4x - 9 = 3
+9 +9
4x = 12
x = 3
Now you have to substitute 3 back into the equation for PQ:
6(3) - 9
18 - 9
= 9
Resulting in PQ = 9, to check your answer, take the value of x (3) and substitute it into PR and you should also get 9
2(3) + 3
6 + 3
= 9
Related Questions
Find the equation of the line that passes through (0, -3) and is parallel to
the line joining the points (9, 2) and (3, -5).
Answers
Answer:
y = [tex]\frac{7}{6}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )
m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]
• Parallel lines have equal slopes , so
m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line
Hey there!
[tex] \\ [/tex]
Answer:[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]
[tex] \\ [/tex]
Explanation:To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .
[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]
[tex] \\ [/tex]
⇒Subtitute the values :
[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]
[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]
[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]
[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:
[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]
[tex] \\ [/tex]
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If your player is Erik, write an inequality that shows all of the ways that Erik will win
if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways
that Nita will win if Erik chooses 17.
Answers
An inequality that shows all of the ways that Nita will win if Erik chooses 17 is
Eric will win if Nita chooses 7 and he chooses and number that is less than 17 (ex. n<17).Nita will win if Eric chooses 17 and she chooses a number less than 8 (ex. n<8).What is an Inequality?This refers to the relation in mathematics that makes an unequal comparison between two numbers or expressions.
Therefore, according to the rules of the game, they would have to make random selections from 0 to 20 and if the difference between their two numbers is less than 10, then Erik wins, the inequality that would show all of the ways that Nita will win if Erik chooses 17 are listed above.
Hence, we can see that the complete question goes thus:
"Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins.
Use what you know about inequalities and absolute values to better understand the game."
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help me answer this table problem please
Answers
By using the concepts of relations and functions and based on the table given, the function presents the following relationship:
x → f(x)
7 → 95
How to evaluate a function according to a table
Functions are relations between an input set named domain (x) and an output set named range (f(x)), that is:
x → f(x)
After a quick observation, for x = 7, then f(7) = 95. In more graphically manner, the function present the respective relation:
7 → 95
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Solve the equation and provide all steps ¾ x+2¼ =9
Answers
Answer:
x=9
Step-by-step explanation:
3/4x+2 1/4=9
3/4x=9-2 1/4
3/4x=6 3/4
4(3/4x)=4(6 3/4)
3x=27
x=9
Answer:
x = 9
Step-by-step explanation:
3/4 x + 2 1/4 = 9 subtract 2 1/4 from both sides of the equation
3/4 x = 6 3/4 now divide both sides by 3/4
x = 9
what is the equation of the given line in the point -slope form
Answers
Answer:
E
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line
m = [tex]\frac{4-1}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
using (a, b ) = (3, 4 ) , then
y - 4 = 1 (x - 3) → E
Donna sells pencils for $2 and pens $3. She sold 11 items and made $30. How many pens did she sell ?
Answers
Donna sold 3 pencils and 8 pens solved using simultaneous equation
What is a simultaneous equation?
Simultaneous equation refers to related equations that are solved at the same to derive answers to the unknown variables
Let assume that X pencils were sold and Y pens were sold
The total revenue is the sum of the prices multiplied by the quantities sold.
2X+3Y=30 (equation 1)
The sum of X and Y sold is 11
X+Y=11 (equation 2)
multiply the second equation by 2
2*(X+Y=11)
2X+2Y=22 (equation 3)
subtract equation 3 from 1
(2X+3Y=30)-(2X+2Y=22)
Y=8
Substitute for Y in equation 2
X+8=11
X=11-8
X=3
Which means he sold 3 pencils and 8 pens.
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Answer:
8
Step-by-step explanation:
Accordding to this function
What is:-
limf(x)
x approches 2⁺
Answers
Answer:
Limit does not exist
Step-by-step explanation:
This is a piece-wise function, since we are finding the limit of f(x) when x is approaching 2 from the right, we know that x must be more than 2. However, based on the piece-wise function, there is no function that satisfy this condition, therefore the limit does not exist for this piece-wise function
The main floor of Kinsey's home is 1,425 square feet. The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet. The finished basement is 1,425 square feet with 7.5-foot ceilings. Kinsey's MLS listing includes below-grade square footage in livable area. What's the reportable square footage for Kinsey's home
Answers
The reportable square footage for Kinsey's home = 2150square feet.
The main floor of Kinsey's home is 1,425 square feet.
The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.
The finished basement is 1,425 square feet with 7.5-foot ceilings.
That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).
Kinsey should report square feet (1425+875- 150)
= 2150square feet.
Hence, The reportable square footage for Kinsey's home = 2150square feet.
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The function g(x) is graphed.
On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).
Which statements about the function are true? Choose three options.
Answers
The statements about the function that are true include:
g(0) = 0
g(1) = -1
g(-1) = 1
How to depict the function?From the information, the points include:
(x1, y1) = (-2, 2, 5).
(x2, y2) = (0, 0)
(x3, y3) = (2, 3, 5).
It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in the graph.
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Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be:
Answers
Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be 7.01 billion.
To calculate the percentage increase rate, use the fundamental increase charge formulation: subtract the original from the brand new cost and divide the results by way of the original cost. to show that right into a percent boom, multiply the results by 100.
The population of a given area is described as the range of humans generally residing in that vicinity, measured on 1 January in a given 12 months. The supply can be the most latest population census.
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If f = 36 when a = 9, find f when a = 8
Answers
Answer:
2=A
Step-by-step explanation:
We know that F is directly proportional to A then the equation relating them is
F = kA ← k is the constant of proportion
To find k use the condition F = 36 when A = 9, then
36 = 9k ( divide both sides by 9 )
4 = k
F = 4A ← equation of proportion
When F = 8, then
8 = 8A ( divide both sides by 4 )
2 = A
PLEASE HELP ME I WILL MARK CORRECT ANSWER BRAINLIEST
Answers
Answer:
36 units
Step-by-step explanation:
to do this you must first find the lengths of all the sides with pythagorean theorem
for a to b you use
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = 5
5 is one of the lengths
b to c uses the same equation
so
5 is another one of the lengths
for d to c your equation is
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 is another of the lengths
d to a has the same length as c to d so there is another 13 unit length
so
5 + 5 + 13 + 13 is your equation to find the perimeter
5 + 5 + 13 + 13 = 36
that is your answer
What type of triangle is shown below?
31°
28.5
19.2
109°
40%
991
Answers
Answer:
could u send a photo please
Can you help me please
Answers
Answer: Option D
[tex]\displaystyle d=\frac{C}{\pi}[/tex]
Step-by-step explanation:
To solve the formula for d, we will isolate the d variable.
Given:
C = πd
Divide both sides of the equation by π:
[tex]\displaystyle\frac{C}{\pi}=\frac{\pi d}{\pi}[/tex], [tex]\displaystyle\frac{C}{\pi}=d[/tex]
Reflexive property
[tex]\displaystyle d=\frac{C}{\pi}[/tex]
b) In the last year, the average rainfall in Pokhara valley during the first 6 months was 150 mm and the average rainfall of the remaining months was 60 mm. Find the average rainfall of the whole year. The average selling of the first 4 days of a shop in the last week was c) Rs 425 and the average selling of the remaining days was Rs 250. Find the average selling of the shop in the whole week. a) Shashwat obtained an average marks of 15 in 3 subjects. When the marks obtained in another subject is also included, the average marks is increased by 1. Find the marks obtained in the fourth subject. b) The average marks of English, Nepali, Science and Social Studies obtained by Sunayana is 70. If the marks obtained in Mathematics is also included, the average marks is increased by 5. Find her marks in Mathematics. eative Section - B The a . b ) In the last year , the average rainfall in Pokhara valley during the first 6 months was 150 mm and the average rainfall of the remaining months was 60 mm . Find the average rainfall of the whole year . The average selling of the first 4 days of a shop in the last week was c ) Rs 425 and the average selling of the remaining days was Rs 250. Find the average selling of the shop in the whole week . a ) Shashwat obtained an average marks of 15 in 3 subjects . When the marks obtained in another subject is also included , the average marks is increased by 1. Find the marks obtained in the fourth subject . b ) The average marks of English , Nepali , Science and Social Studies obtained by Sunayana is 70. If the marks obtained in Mathematics is also included , the average marks is increased by 5. Find her marks in Mathematics .
Answers
Answer:
For b), the answer is 105mm
Step-by-step explanation:
(150+60)/2
What polynomial function could be represented by the graph below
(A). F(X)=x^2+x-2
(B). F(X)=2x^2+2x-4
(C). F(X)=x^2-x-2
(D). F(X)=2x^2-2x-4
Answers
Answer:
(B). F(X)=2x^2+2x-4
Step-by-step explanation:
-4 means it passes through -4 at the y axis
B and D have -4
graph passes thru x axis at -2 and 1
if you enter x = -2 or 1 in the formula
(B). F(X)=2x^2+2x-4
you get 0
it's not D because when you enter -2 or 1 for x
you don't get 0
you get 8 and -4
Answer: (B). F(x) = 2x² + 2x - 4
Step-by-step explanation:
Let us think about the parent function F(x) = x² to pick our answer.
Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.
Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.
What is the value of (-5)^4
Answers
Answer:
-20
Step-by-step explanation:
-5-5-5-5=-20
For how many values of x does the graph f(x)= x^2 -3 intersects the x-axis?
Answers
Answer:
cocomelon . 3/5 - 4
Step-by-step explanation:
Answer:
x=[tex]\sqrt3[/tex] and -[tex]\sqrt3\\[/tex]
Step-by-step explanation:
the roots(zeros) are the value of x where the graph intersects the x-axis.
to find the roots:
x^2-3=0
x^2=3
x=+-[tex]\sqrt3[/tex]
The supplement of a 162 degree angle is an angle that measures
Answers
Answer:
18 degrees
Step-by-step explanation:
Supplementary angles are angles that when added together equal 180 degrees.
A + 162 = 180
- 162 -162
A = 18
Answer:
18
Step-by-step explanation:
When your are asked the supplement you minus 162 from 180. When you join SU from supplement and add a 1 behind SU you'll get 180. [1SU TO 180]
180-162
18
Evaluate the expression using x=-1 and y=3 (6^4y^3)
Answers
The value of the expression when evaluated is: 162.
How to Evaluate an Expression?To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.
6(-1^4) × 3^3
6(1) × 27
6 × 27
162
The value of the expression, 6x^4y^3, is: 162.
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For the following exercises, find the x- and y-intercepts of the graphs of each function.
26. f(x) = 4| x − 3 | + 4
Answers
For the function f(x) = 4|x - 3| + 4, we have that:
The function has no x-intercepts.The y-intercept is of y = 16.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = f(x) = 0, hence:
0 = 4|x - 3| + 4
4|x - 4| = -4
|x - 4| = -1
The absolute value cannot be negative, hence the function has no x-intercepts.
What is the y-intercept of a function?The x-intercept of a function is the value of y = f(x) when x = 0, hence:
f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.
The y-intercept is of y = 16.
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5. A bus covers a certain distance in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to reduce the time by 20 minutes.
Answers
Answer:
108 km/hr
Step-by-step explanation:
45 minutes = 3/4 hours
1) Distance = speed × time
= 60 × 3/4
= 45 km
2) 20 minutes = 1/3 hours. So, 3/4 - 1/3 = 5/12 hours.
speed = distance / time
= 45 / 5/12
= 108 km/hr
4.751 4.373 4.177 4.676 (a) Construct a confidence interval for the mean rate. Round the answer to at least four decimal places. A confidence interval for the mean rate is
Answers
98% confidence interval for the mean rate = [4.1437 , 4.4983]
We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;
4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414
Now, Firstly we will find the Mean of the above data, Xbar ;
Mean, Xbar = ∑ x ÷ n =
4.751 + 4.373 + 4.177 + 4.676 + 4.425 + 4.228 + 4.125 + 4.251 + 3.951 + 4.192 + 4.291 + 4.414 ÷ 12 = 4.321
Standard deviation, s = √ ∑(x - x bar)²÷ n-1 = 0.226.
Now, the pivotal quantity for the 98% confidence interval for the mean rate is;
P.Q = x bar - ц ÷ n - 1 ≈ tn - 1
where, Xbar = sample mean
s = sample standard deviation
n = sample size = 12
So, 98% confidence interval for the mean rate, μ is ;
P(-2.718 < t₁₁ <2.718) = 0.98
P(-2.718 <Xbar - μ σ√ⁿ < 2.718) = 0.98
P(Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar + 2.718 * ₈÷ √ⁿ ) = 0.98
98% confidence interval for μ = (Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar + 2.718 * ₈÷ √ⁿ ) = 0.98
[4.321 - 2.718 * 0.226 ÷ √₁₂ , 4.321 + 2.718 * 0.226 ÷ √₁₂
= [4.1437 , 4.4983]
Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]
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Can someone pls help me with this problem?
Answers
For the first blank, since the output increases by 5 for each increase of 1 for the input, the answer is 13+2(5) = 23.For the second blank, since the output increased by 10 compared to 23, the input increased by 2. So, the answer is 5 + 2 = 7.We know the output is of the form 5x+b for some constant b. If we test input of 1 and an output of 3, we get an input of 1 gives 5+b, which is equal to 3, meaning b=-2. So, the answer is 5x-2.
help me i dont understand this
Answers
All functions are relations, but not all relations are functions
Collect Data from Our Solar System
Fill in the table. To obtain each planet's distance from the sun
Answers
Answer:
jupiter, Saturn, Uranus, neptune are all distance from sun
Step-by-step explanation:
Answer:
AU:
Merc-0.39
Venus-0.72
Earth- 1
Mars- 1.52
Jupiter - 5.20
Uranus - 19.1
Neptune - 30
Years:
Merc-0.24
Venus-0.61
Earth- 1
Mars- 1.88
Uranus - 84?(maybe)
Neptune - 165
Step-by-step explanation:
Edge
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$300 and $350.
[? ]%
Answers
Answer:
0.1359
Step-by-step explanation:
Triangle PQR is transformed to similar triangle P’Q’R’
What is the scale factor of dilation?
1/2
1/3
1/4
1/5
Answers
Scale factor = (image)/(preimage)
[tex]QR=3\\\\Q'R'=1[/tex]
So, the scale factor is 1/3
Points u, m, and d are collinear with m between u and d. given um=5x+30 md=3x+80 ud=10x+20
Answers
The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.
What is the required lengths ?Given that, um=5x+30
md=3x+80
ud=10x+20
We know that m is the midpoint of ud
Thus, um + md = ud
5x+30 + 3x+80 = 10x+20
5x+3x + 30+80 = 10x+20
8x + 110 = 10x+20 (taking terms with x to one side of equation)
10x - 8x = 110 - 20
2x = 90
⇒ x = 45
Therefore the lengths,
um=5x+30 = 5(45)+30 = 225 + 30 = 255
md=3x+80 = 3(45)+80 = 135 + 80 = 215
ud=10x+20 = 10(45)+20 = 450 + 20 = 470
Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.
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6.
f(a+h)-f(a)
Determine
h
Of(a+h)-f(a)
h
Of(a+h)-f(a)
h
Of(a+h)-f(a)
h
=
for f(x) = x2 + 5x and simplify.
=
2a + h + 5
h
= 2a + 2h+5
2ah + h² - 5a
h
Of(a+h)-f(a) = 2a + h + 5
h
Answers
The value of the function operation f(a + h) - f(a) is; h² + 5h + 2ah
How to simplify functions?We are given the function;
f(x) = x² + 5x
We want to find f(a + h) - f(a)
Let us first find f(a + h) to get;
f(a + h) = (a + h)² + 5(a + h)
⇒ a² + 2ah + h² + 5a + 5h
⇒ a² + 5a + h² + 5h + 2ah
Let us now find f(a) to get;
f(a) = a² + 5a
Thus, f(a + h) - f(a) = a² + 5a + h² + 5h + 2ah - a² - 5a
f(a + h) - f(a) = h² + 5h + 2ah
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