The equations of the lines that pass through the point (0,5) and intersect the circle at exactly one point are y = 4/3x + 5 and y = -4/3x + 5.
The equation of a circle centred at the origin with a radius of 3 units is defined by x² + y² = 3². The coordinates of the point are (0, 5). Let the equation of the tangent be y = mx + c.
y = mx + c
5 = m(0) + c
c = 5
The equation of the tangent is of the form mx -y + 5 = 0. The distance of the centre of the circle from the tangent must be equal to the radius of the circle.
d = |ax + by + c|/√(a² + b²)
3 = |m(0) + (-1)(0) + 5|/√[m² + (-1)²]
√[m² + (-1)²] = 5/3
m² + 1 = 25/9
m² = 16/9
m = ±4/3
The equations of the tangents are y = 4/3x + 5 and y = -4/3x + 5.
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Solve x2 − 4x − 1 = 0 by completing the square.
Hello! To solve completing by the square, we have to follow some steps:
[tex]\begin{gathered} x^2-4x=1 \\ \end{gathered}[/tex]Now, we have to add the same value in both sides (square):
If we factorize the first part of this expression, we can obtain:
Notice that we obtained the same expression, and now we know the value of the square. So, let's rewrite the first expression and replace the squares by 4:
Beginning with the equation x=-27 write the new equation produced by dividing both sides by 3
Answer:
[tex]\frac{x}{3}=-9[/tex]
The point (3,-1)( 3 , − 1 ) is a solution to this system of equations:
The system of equations we have is:
[tex]\begin{gathered} -3x-2y=-7 \\ x+4y=1 \end{gathered}[/tex]And we need to check if the point (3,-1) is a solution.
Step 1. Identify the values of x and y from the point.
In a point, the first number represents the x-value, and the second number represents the y-value. So in point (3,-1) 3 is the x-value, and -1 is the y-value:
[tex]\begin{gathered} x=3 \\ y=-1 \end{gathered}[/tex]Step 2. Substitute the x and y-value into the first equation and check that the result is equal to -7.
The first equation is:
[tex]-3x-2y=-7[/tex]Substituting x=3 and y=-1:
[tex]-3(3)-2(-1)=[/tex]Solve the operations:
[tex]-9+2=-7[/tex]Since we get -7 as the result, (3,-1) is a solution for the first equation. But we still need to check if the point is a solution for the second equation.
Step 3. Substitute the x and y values into the second equation and check that the result is 1.
The second equation of the system is:
[tex]x+4y=1[/tex]Substituting x=3 and y=-1:
[tex]3+4(-1)=[/tex]Solving the operations:
[tex]3-4=-1[/tex]The result we get is -1, not 1. Thus, since the point (3,-1) is not a solution for the second equation, it is also not a solution to the system of equation.
Answer: False
what tip of function line exponential or quadratic best models in each table
This makes the correct answer to be exponential function
What is the equation of the line in slope-intercept form?
Answer:
5/2; 5
Step-by-step explanation:
The first box is m, which is the slope. To find the slope you do rise over run, so basically the change in x and y. You move up 5 and over 2, so m would be 5/2.
The second box is b, which is the y-intercept. To find the y-intercept, you just find where the line crosses the y-axis. That would be 5
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
The weights of the melons harvested from a patch are distributed normally. The mean weight is 6 pounds; the standard deviation is 0.25 pounds. Which is closest to the percent of melons that weigh 6.25 pounds or less?A) 34B) 68C) 84D) 98
As it is normally distributed, we can use Z to find the result.
Procedure
0. Finding the value of ,Z
[tex]Z=\frac{x-\mu}{\sigma}[/tex]1.2. Replacing the values given in the problem:
[tex]Z=\frac{6.25-6}{0.25}[/tex][tex]Z=\frac{0.25}{0.25}=1[/tex]2. As it is normally distributed:
[tex]P(x\le6.25)=P(Z\le1)[/tex]3. Using the normal standard table, we can conclude:
[tex]P(Z<1)=0.8413[/tex]As it is asking for a percentage, we multiply by 100.
Answer: C) 84%
While digging in his garden Will pushes a shiv into the ground with a force of 585 newtons at an angle of 80° with the ground
Force, F = 585 N
Angle, θ = 80°
The diagram that shows the resolution of the force into its rectangular component is drawn below
The magnitude of the horizontal component is:
[tex]\begin{gathered} F_x=585\sin 80 \\ F_x=585(0.9848) \\ F_x=576N \end{gathered}[/tex]The magnitude of the vertical component is:
[tex]\begin{gathered} F_y=585\cos 80 \\ F_y=585(0.174) \\ F_y=102N \end{gathered}[/tex]Therefore, the magnitudes of the horizontal and vertical components of the force are (576, 102)
Credit Card Statement Calculate the newPrevious Balance $120.00 balance on thisFinance Charge $15.00 account after theseNew Purchases $200.00 charges andPayments $(300.00) payments areCredits$0.00applied.A. $35.00B. $635.00C. $235.00D. $395.00
Previous Balance: $120
Finance Charge: $15
New Purchases: $200
Payments: $300
Recall this is a Credit Card Statement.
To find the new balance we must subtract the payments and add the charges:
New Balance = $120 - $300 + $15 + $200
New Balance = $35
Answer: A. $35.00
The cat of a play had a party. The drama teacher erved 20 cookie and 40
carrot tick a refrehment. Each cat member ate the ame number of
whole cookie and the ame number of whole carrot tick. Nothing wa left
over. The drama teacher did not eat. How many cat member might have
been at the party? Explain
Given two quantities (number of cookies and carrot sticks), we find the greatest common divisor (gcd) to know that were 20 cast members at the party. Below is a solution algorithm written in Python.
The Solution Algorithmif __name__ == '__main__':
# Define variablesa = int()
b = int()
x = int()
gcd = int()
# Number of cookies
a = 20
# Number of carrot sticks
b = 40
# Calculate the greatest common divisor (gcd) between the number of cookies and the number of carrot sticksgcd = 1
x = 1
while x<=a:
if a%x==0 and b%x==0:
if x>gcd:
gcd = x
x = x+1
# Displaying resultsprint("Number of cookies: ",a)
print("Number of carrot sticks: ",b)
print("Number of cast members at the party: ",gcd)
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question provided in picture only need assistance with part b
PART B
The probability is 1/2
STEP - BY - STEP EXPLANATION
What to find?
The probability of identical twins given that the twins consists of two boys.
Let A be the event of identical twins.
Let B be the event of having two boys as twins.
From the table given;
P(A) = 2/38
P(B)= 2/38
Recall the formula for a condititional probabibility
[tex]P(A\text{ \backslash{}B)=}\frac{P(A\text{ n }B)}{P(B)}[/tex]Note that:
P(A n B) =1/38
[tex]P(A\text{ \backslash B) =}\frac{\frac{1}{38}}{\frac{2}{38}}[/tex][tex]=\frac{1}{38}\times\frac{38}{2}[/tex][tex]=\frac{1}{2}[/tex]Therefore, the probability of identical twins given that the twins consists of two boys is 1/2
Find the value of x in x + y = 9 and x - y = 2.5.553.5-5.5
Step 1
Given; Find the value of x in x + y = 9 and x - y = 2.
Step 2
Using the elimination method.
[tex]\begin{gathered} x+y=9 \\ + \\ x-y=2 \\ --------- \\ 2x\text{ +0=11} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 2x=11 \\ x=\frac{11}{2} \\ x=5.5 \end{gathered}[/tex]Answer;
[tex]x=5.5[/tex]Function A represents the amount of money in a jar based on the number of quarters in the jar. Function B represents your distance from home over time. Compare the domains.
The domains of each function are classified as follows:
Function A: Discrete domain.Function B: Continuous domain.What is the domain of a function?
The domain of a function is the set composed by all the input values that are assumed by the function.
For each function in this problem, the inputs are given as follows:
Function A: number of quarters in the jar.Function B: time.Hence, the domain of function A is a discrete domain, as the number of quarters in the jar can assume countable values such as 0, 1, 2, ..., it does not assume decimal values.
For function B, the domain is a continuous domain, as measures of time can assume decimal values, for example, 10.5 minutes.
These differences discussed represent the comparison of the domains of each function.
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Mr. Jensen purchased an airline ticket on a web site. The original price of the airline ticket was $473.00. He used a coupon code to receive a 20% discount. A sales tax of 12% was applied after the discount. What was the total purchase price of the airline ticket after the discount, including sales tax?
A $105.92
B $332.99
C $423.81
D $529.76
The price of the online ticket after discount, including sales tax, is $423.81.
What is percentage?Percentage is a measurement to find the value of a given number out of a hundred.
Given that,
The original price of the airline ticket = $473
Discount after applying coupon code = 20%
The price after applying coupon code = 473x4/5 = 378.4
Since, there is a sales tax of 12%,
So the price of airline ticket after sales tax = 378.4 x 112/100 = 423.808
The price of online ticket after discount and including sales tax is $423.81
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Explain step by step how to complete -0.7 = 9.1
Answer:
9.1.4 -0.7=9.1
Step-by-step explanation:
Step 1: Determine the Assessment Unit ID (AUID) of the waterbody of interest.
Step 2: Express the quadratic equation in standard form
write the line, in slope-intercept form,that is (a) parallel and and (b) perpendicular to the line 4x +2y=6 that passes through the point (2,6).
We have the following equation given:
[tex]4x+2y=6[/tex]If we solve in the form y=mx+b we got:
[tex]y=-2x+3[/tex]Part a
S
HELP QUICK PLS!!
State all integer values of x in the interval -4 ≤ x ≤ 3 that satisfy the following inequality:
-5x - 3 > 8
Answer:
[tex]-4 \leq x < -2.2[/tex]
Step-by-step explanation:
-5x - 3 > 8
-5x > 11
x < -11/5
We know that -4 ≤ x ≤ 3 and x < -11/5 (-2.2)
-4 <= x < -2.2
A box of fruit has four times as many oranges as grapefruit. Together there are
60 pieces of fruit. How many pieces of each type of fruit are there?
The number of mangoes = 48
The number of grapefruit = 12
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A box of fruit has four times as many oranges as grapefruit.
And, Total number of fruit = 60 pieces
Now,
Let number of grapefruit = x
Then, Number of Mangoes = 4x
So, We can formulate;
⇒ x + 4x = 60
Solve for x as;
⇒ 5x = 60
⇒ x = 12
Thus, Number of grapefruit = x
= 12
Then, Number of Mangoes = 4x
= 4 × 12
= 48
Therefore, The number of mangoes = 48
The number of grapefruit = 12
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Write the fractions in order from greatest to least 1/4 3/6 1/8
3/6, 1/4, 1/8
Step-by-step explanation:
All three fractions have a common denominator of 24.
1/4=6/24
3/6=12/34
1/8=3/24
Lastly, order them from greatest to least, hence 3/6, 1/4, and 1/8
Seven times the quotient of x and 9 added to 2
gives
25. What is x?
After making and solving an equation, we can say that the value of x is 1.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.Like this: 2x - 4 Equals 2. In the above example, the variable x exists.So, to find the value of x, we will solve the equation:
7(x/9) + 2 = 25/9
Now, solve this equation as follows:
7(x/9) + 2 = 25/9
7x/9 = 25/9 - 2
7x/9 = 7/9
x = 1
Therefore, after making and solving an equation, we can say that the value of x is 1.
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PLS SOMEONE HELP ME OUT ASAP
The results of the transformations carried out are respectively;
1) Preserves only angles but not distance
2) Preserves both angles and distance.
3) Preserves only angles but not distance
How to Interpret Transformation of Objects?
In transformations, there are different types such as dilation, reflection, translation, rotation, e.t.c
1) Dilation of a quadrilateral by a scale factor of 2;
When we dilate by a scale factor of 2, it simply means we are enlarging the side lengths by a scale factor of 2. Thus, the side lengths will increase but angles remain the same.
2) Translation of a rhombus 3 units to the right and then a reflection across the x-axis;
When we translate an object, it means we just move it from one point to the other and this means that the length and angles do not change, Similarly, reflection is just a mirror image and it also means that the length and angles do not change.
3) Translation of a triangle 2 units to the left and then a dilation by a scale factor of 5 about the origin;
This will end up changing the side lengths but not the angles.
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The radius of a circle is 18 ft. Find its área un terms of pi
Answer
Area = 324π ft²
Explanation
The area of a circle is given as
Area = πr²
where
π = pi
r = radius of the circle = 18 ft.
Area = πr²
Area = π (18²)
Area = 324π ft²
Hope this Helps!!!
A tennis star was hired to sign autographs at a convention. She was paid 3000 plus 2% of all admission fees collected at the door. The total amount she received for the day was 3540. Find the total amount collected at the door
Let x be the total amount collected at the door. Then, we can write
[tex]3000+(0.02\times x)=3540[/tex]where the 0.02 denotes the comission of 2%. From this equation, we can find x.
Then, by moving 3000 to the right hand side, we have
[tex]\begin{gathered} 0.02x=3540-3000 \\ \end{gathered}[/tex]which gives
[tex]0.02x=540[/tex]Now, by moving 0.02 to the right hand side, we get
[tex]x=\frac{540}{0.02}[/tex]then, x is given by
[tex]x=27000[/tex]Therefore, the total amount collected at the door is $ 27 000.
What is the value of x?
A) x=15
B) x=22
C) x=12
D) x=20
Answer: It would be c x=12
Step-by-step explanation:
(13.9 x 108) - (2 x 102
Answer
Answer = (6.95 × 10⁻¹⁰)
Explanation
We are asked to solve (13.9 × 10⁻⁸) ÷ (2 × 10²)
To solve this, we will have
[tex]\begin{gathered} \frac{13.9\times10^{-8}}{2\times10^2}=\frac{13.9}{2}\times\frac{10^{-8}}{10^2}=6.95\times10^{-8-2} \\ =6.95\times10^{-10} \end{gathered}[/tex]Hope this Helps!!!
You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The arch over the road is in the shape of a half-ellipse that is 40 feet wide at the base of the arch and it is 15 feet tall at the center of the arch. The bridge must have a 13-foot clearance for vehicles on the road. The 22-foot-wide road is centered directly beneath the highest point of the arch. a) the semi-truck will NOT be able to pass under the bridge,so it is time to make an adjustment. You will need to modify the design of the bridge. Keep the arch shape as half an ellipse, and the base as 40 feet wide. You may adjust the bridge’s arch up to 18 feet above the center line of the two-lane road below, but no more than that because of restrictions concerning the road crossing over the bridge. Give a new equation for the ellipse that represents your modified design.
We are asked to determine the equation of an ellipse that has a base of 40 feet and a height of 18 feet. This can be visualized in the following diagram:
The general form of the equation of an ellipse is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]We have set the origin of the coordinate system to be in the middle of the ellipse. The value of "a" is the x-intercept of the ellipse and the value of "b" is the y-intercept of the ellipse. Therefore, the equation is:
[tex]\frac{x^2}{(20)^2}+\frac{y^2}{(9)^2}=1[/tex]Now, we solve the squares:
[tex]\frac{x^2}{400}+\frac{y^2}{81}=1[/tex]And thus we have determined the equation of the ellipse.
Asif can use the greatest common factor to rewrite 28+49 as (4+ ).
Answer:
7*(4 + 7)
Step-by-step explanation:
28 = 7 *4
49 = 7 * 7
GCF = 7
28 + 49 = (7*4) + (7*7)
= 7*(4 + 7)
In 2.073, in which place is the 7?
Answer:
Step-by-step explanation:
tents is what place it is <3
If a_1=6a
1
=6 and a_n=a_{n-1}+3a
n
=a
n−1
+3 then find the value of a_4a
4
.
The fourth term a₄ of the sequence is 15
How to determine the value of a₄?The definition of the function is given as
a₁= 6
aₙ = aₙ₋₁ + 3
The above definitions imply that we simply add 3 to the previous term to get the current term
using the above as a guide,
so, we have the following representation
a₂ = 6 + 3
a₂ = 9
Also, we have
a₃ = 9 + 3
a₃ = 12
Lastly, we have
a₄ = 12 + 3
Evaluate the equation
a₄ = 15
Hence, the value of a₄ is 15
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112+18x14+14-14=
OA) 12
O B) 18
O C) 116
O D)130
A mathematical "operation" is the process of calculating a value using operands and a math operator.
If the equation be 112 + 18 × 14 + 14 - 14 by simplifying the calculation, we get 364.
What is meant by mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
A mathematical "operation" is the process of calculating a value using operands and a math operator. There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.
Let the equation be 112 + 18 × 14 + 14 - 14
= 112 + 252 + 14 - 14
Add and subtract (left to right)
112 + 252 + 14 - 14 = 364
Therefore, by simplifying the above calculation, we get 364.
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