The equation of line tangent is y-35x+30=0.
What is tangent of a line?
A tangent line to a circle is a line that touches the circle exactly one time in Euclidean plane geometry and never enters the interior of the circle. Tangent lines to circles are the focus of various theorems and are crucial to numerous geometric structures and mathematical arguments.
Given equation y=2x+33x-2
=>y=35x-2
General slope intercept form is y=mx+b
Comparing and we get m = 35
The equation of tangent is y-5=35 (x-1)
=> y-5=35x-35
=> y=35x-35+5
=>y-35x+30=0
Therefore, the equation of line tangent is y-35x+30=0.
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find L.C.M of 90 and 108
Which is the 7 th number in this pattern?
8,13,18,23,. . .
(F) 28
(G) 33
(H) 38
( I ) 43
Answer:
38
Step-by-step explanation:
well done .....I hope it's helpful
a line segment has endpoints at A(-7,11) and B(5,-5). Point O lies on the line segment. Which coordinates for point O result in the ratio of AO to BO of 3:1?
The coordinate for point O so that it divides AB in the ratio of AO to BO as 3:1 is (2, -1)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The line segment has endpoints at A(-7,11) and B(5,-5). Point O(x, y) divides the segment AB in the ratio 3:1, hence:
x = (3 / (3 + 1))[5 - (-7)] + (-7) = 2
y = (3 / (3 + 1))[-5 - 11] + 11 = -1
The coordinate for point O so that it divides AB in the ratio of AO to BO as 3:1 is (2, -1)
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Answer: (-4,7)
Step-by-step explanation:
you have to use distance formula
Jesse has been saving his earnings from his lemonade stand. Jesse has 47 dollars to spend. If He buys a new hat for 19 dollars, how many scarves can He buy with the remaining spending money if they cost 7 dollars each?
Answer: 4 scarves.
Step-by-step explanation: $47-$19= 28. 28 divided by $7 is 4, so Jesse could buy 4 scarves with the remaining money.
What is the 25th term in the sequence 11, 20, 29, 38, 47…?
The 25th term in the sequence 11, 20, 29, 38, 47… is 227.
How to calculate the sequence?Based on the information illustrated, it should be noted that the 25th term in the sequence 11, 20, 29, 38, 47… will be calculated thus:
In this case, this is an arithmetic sequence. The formula to calculate the sequence will be:
= a + (n - 1)d
a = first term = 11
d = common difference = 9
The 25th term will be:
a + (n - 1)d
= 11 + (25 - 1)9
= 11 + (24 × 9)
= 11 + 216
= 227
The 25th term is 227.
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A medical insurance policy requires Ana to pay the first $100 of her hospital expense. The insurance company will then pay 90% of the remaining expense. Ana is expecting a short surgical stay in the hospital, for which she estimates the total bill to be about $4,700. How much (in $) of the total bill will Ana owe
The total bill that Ana would pay is $560.
What is the total bill Ana would pay?The total bill that Ana owes is the sum of the first $100 and 10% of the remaining bill since the insurance company would pay 90% of the bill.
The mathematical operation that would be used to determine the total bills are addition, multiplication and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of calculating the difference between two or more numbers. Multiplication is the process of determining the product of two or more numbers.
Total bill = first $100 + 90%(total bill - $100)
$100 + 10%($4,700 - $100)
$100 + 10% x 4,600
$100 + (0.1 x 4,600)
$100 + $460
$560
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1 Dɔntrez had 1/2 lb of trail mix. Each day, he took 1/8 lb of trail mix to
=chool for a snack. If he had 1/4 lb of trail mix left over, how many days did
Dontrez take trail mix to school?
For your answer, ONLY type the number and your word label.
Your answer
Dontrez took 1/8 lb fraction of trial mix to school for only 2 days.
What is a fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator, displayed above a line, and a non-zero denominator, displayed below that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
Dontrez took 1/8 lb fraction of trial mix to school for only 2 days.
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Please helppp due soon
Shelly picked out a pair of jeans to purchase that are marked $54.99. She has a coupon that gives her $10 off. She has a SPC card that gives her an additional 10% off the total cost before taxes. What will she pay for the jeans including 13% tax?
Answer:
assuming the coupon came b4 everything else : $ 45.75
Step-by-step explanation:
ten off of 54.99 is 44.99
10 % of 44.99 is 4.499
44.99 - 4.499 is 40.49
13% of 40.49 is 5.26
so 40.49 + 5.26 is 45.75
I need help thnx :))))))))
Answer:
the answer is -2
Step-by-step explanation:
I hope this helps! :)
a. The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contain 200 Calories, how many Calories are in 70 grams of cheese?
If 50 grams of cheese contain 200 Calories, 280 kcal are in 70 grams of cheese.
50g = 200 kcal
1g = 200 kcal / 50g
70g = (200 kcal / 50g) × 70g
= 280 kcal
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Consider a utility function that represents preferences over perfect complements: (1,2)=min{341,172}u(x1,x2)=min{34x1,17x2}.
According to the question, the utility function can be written as: [tex]U(x,y)=min(341,172)[/tex]
What is utility function and perfect complements?
A utility function is a standard rule which is assigned to all consumption bundles. And it is represented as two good models which are known as domain and codomain. It is also used to represent the individual items for the goods or services beyond their monetary value. Similarly, when two goods are consumed perfectly then they are called perfect complements.
Similarly, Perfect complement is: [tex]max(341,172)[/tex]
Therefore, the equations can be written for the points(1,2):
[tex]x_{1} +2x_{2} =172[/tex] and [tex]x_{1} +x_{2} = 341[/tex]
And the calculated equation is perfect complements:
[tex]x_{1} +2x_{2} =172[/tex] and [tex]x_{1} +x_{2} = 341[/tex]
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Read each question. Then write the letter of the correct answer on your paper.
What are the first five terms of the sequence a n =2 n-1 ?
(F) 0,1,2,3,4
(G) 1,3,5,7,9
(H) 2,4,6,8,10
(I) 3,5,7,9,11
The first five terms of a sequence with explicit formula a(n) = 2n - 1 are 1,3,5,7,9 (G)
An arrangement of numbers with particular pattern is called a sequence. In general, there are four types of sequence: arithmetic sequence, geometric sequence, quadratic sequence, and special sequence.
Suppose we are given an explicit formula for the nth term of a sequence, then its terms can be evaluated by substituting n = 1, 2, ...
The explicit formula of the given sequence:
a(n) = 2n - 1
Take n = 1, then
a(1) = 2.(1) - 1 = 1
Take n = 2, then
a(2) = 2.(2) - 1 = 3
Take n = 3, then
a(3) = 2.(3) - 1 = 5
Take n = 4, then
a(4) = 2.(4) - 1 = 7
Take n = 5, then
a(1) = 2.(5) - 1 = 9
Hence, the first five terms are 1,3,5,7,9 (G)
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6.13 round each number to the place of the underlined dight 1
Answer: 6.1
Step-by-step explanation:
If the digit after the underlined digit is 4 or less, then you round down. If the digit after the underlined digit is 5 or more, than you round up.
6.13 rounded to the nearest tenth is 6.1
Preform the indicated operation 5/4 + 7/9
Answer:
5/4+5/9
45/36 +20/36
65/36
1 30/36
Write 0.000493 in scientific notation.
The height of a parallelogram is three times its base. If the area of the parallelogram is 108 square meters, find its base and height.
The base and height of parallelogram is 6 meters and 18 meters.
We are given the relationship between base and height of parallelogram. Let the height be h and base be b. The equation is as follows -
h = 3×b
The formula to calculate area of parallelogram is -
Area = base × height
Keep the values in formula to find the base of parallelogram -
108 = b×3×b
Performing multiplication on Right Hand Side of equation
108 = 3b²
b² = 108÷3
Performing division to find the base of parallelogram -
b² = 36
b = √36
Taking square root of b
b = 6 meters
So, the base of parallelogram is 6 meters.
Height = 3 × 6
Performing multiplication
Height = 18 meters
Hence, the base and height of parallelogram are 6 meters and 18 meters.
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Consider the inequality 38 ≤ bx + 8
What value of b will result in the solution x ≤ - 6?
For the value of (b = -5) the result of the solution is x ≤ - 6.
What is termed as the inequality?The term inequality refers to a mathematical equation wherein the sides are not equal. An inequality equates any two values and shows that one is less, greater, or equal to the value on either side of the equation.
Rule 1: When inequalities are connected, they can be crossed. As a result, if an is greater than b and b is greater than c, a will be greater than c as well.Rule 2: When you swap the values, the sign as well reverses.Rule 3: An inequality can be either > or, but not both at the same time.Rule 4: Reversing the sign by multiplying both sides of the inequality by the a negative sign.Consider the given expression;
38 ≤ bx + 8
Simplify the equation;
38 - 8 ≤ bx
30 ≤ bx
Multiply both side with negative sign; by the rule four, the sign of inequality will also change.
- 30 ≥ -bx
or -bx ≤ - 30
For converting the value to the expression x ≤ - 6; the value which should be divide the 30 is 5.
Thus,
-(-5)x ≤ - 30
Thus, the value of b is found as (b = -5).
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9,369 divided 53 help please
Answer:
the answer is
[tex]176 \times \frac{41}{53} [/tex]
hope this helps
3(x+8)=-6
Pleaseeee do the whole equation line and all
Answer:
x= - 10
Step-by-step explanation:
Divide both sides of the equation by 3, x+8= - 2. move the constant to the right side and change its sign, x= - 2 - 8. Calculate the difference and the solution will be x= - 10
A certain species of fish costs $3.29 each. You can spend at most $25. How many of this type of fish can you buy for your aquarium?
Answer:
7
Step-by-step explanation:
25÷3.29=7.59
you can't buy half a fish and rounding up would go over budget so you buy 7 with a little change left over
Answer:
You can only buy 7.
Step-by-step explanation:
the most you can spend is $25 so you divide 25 by 3.29 which gives us 7.6 but in this case we don't round because you can only spend $25, so you can only buy 7.
When rounded to the nearest thousand, 15,000 soft pretzels were
sold during the game at PNC Park. Write three numbers that could
represent the number of soft pretzels sold.
Answer:
More practically, MORE than $150 is wanted so the answer is 3x-x+2=4
Step-by-step explanation:
Any choice of WHOLE NUMBER divisible by 3 will work for x to give a whole number for y, for acceptable points ON the line; but points found ABOVE the line with whole number coordinates would also be acceptable for this INEQUALITY problem. As example, do you understand that x=27, y=11, will work? It is just one of many, many possible solutions.
The equation the quantity 2x minus 10 divided by 4 = 3x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x. x = −10 x = −1 x = 2 x = 11
Answer:
I'm pretty sure it's -1 but correct me if I'm wrong
Answer: x=-1
Step-by-step explanation:
x=-1
because
2x - 10
over = 3x
4
we can put everything in parentheses and multiply by 4
2x - 10
4( over )= (3x) 4
4
The 4's on the left side will cancel out around and leave
2x - 10
on the right we multiply 3x x 4 which equals 12x
rewrite the equation
2x - 10 = 12x
subtract 2x on each side with the variable.
2x - 10 = 12x
-2x -2x
the 2x's on the left will cancel out.
on the right 12x - 2x equals 10x
now the equation is
-10=10x
but we are not done
divide 10 on each side
on the left -10/ 10 equals -1 because one number is negative and that does not give a postive result.
on the right 10x/ 10 the 10's cancel out leaving the varible x
we are left with
x=-1
Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form.
The indefinite integral, [tex]\int {sin(9x)} \, dx[/tex] = [tex]\frac{-1}{9} cos(9x) + C[/tex]
We have to find the indefinite integral,
[tex]\int {sin(9x)} \, dx[/tex]
using the substitution 9x = u.
So we need to change the variable of integration from x to u using this substitution.
9x = u ⇒ 9 dx = du
So [tex]\int {sin(9x)} \, dx[/tex] = [tex]\frac{1}{9} \int{sin(u) \ du[/tex]
= 1/9 (- cos(u)) + C, [ Since integral of sin(u) = -cos(u) ]
where C is the integration constant which is often put when evaluating indefinite integrals.
Now replacing u with x to get the final answer,
1/9 (- cos(u)) + C = -1/9 cos(9x) + C
Therefore, [tex]\int {sin(9x)} \, dx[/tex] = [tex]\frac{-1}{9} cos(9x) + C[/tex]
The question is incomplete. Find the complete question below:
Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form. [tex]\int {sin(9x)} \, dx[/tex], 9x = u.
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Select the expressions that are equivalent to 7(-7u - 4) - 5.
(-7u - 4)7 - 5
7(-8u+ u 4) - 5
-33u - 49
-7u - 33
Answer: only the first one
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
(A) x2 + (y – 3)² = 36, is the equation that represents circles with a diameter of 12 units and a center on the y-axis.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, the standard form for calculating the equation of a circle is as follows:
(x-a)² + (y-b)² = b = r²
Where;
(a, b) is the circle's center.The radius of the circle is denoted by r.Information:
diameter = 12 unitsradius = 12/2 = 6 unitsIf the center is on the y-axis, it will be at (0, 3).
By substituting into the formula, we get (x-0)² + (y-3)² = 6² is equivalent to
x²+ (y-3)² = 36Therefore, the equation that represents circles with a diameter of 12 units and a center on the y-axis is (A) (A) x2 + (y – 3)² = 36.
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The correct question is given below:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
a. x2 + (y – 3)2 = 36
b. x2 + (y – 5)2 = 6
c. (x – 4)² + y² = 36
d. (x + 6)² + y² = 144
e. x2 + (y + 8)2 = 36
Write the function rule for each function reflected in the given axis.
f(x)=2 x-4 ; x - axis
The given function is f(x) = 2x-4,
We have to find the equation where the reflection of this function is over the x-axis.
There are two types of reflections in general when we talk about functions;
One reflection is over the x-axisThe other is over the y-axis.Now we take an example that we are provided with a point with coordinates (x, y). If we want to reflect it over the x-axis, then the coordinates of this point will become (x, -y). This is because the values of y are negative when we move above the x-axis and positive when we move below the x-axis and vice versa.
The equation to show this is: y = -f(x).
We multiply the entire function, f(x), to find it by a negative. Since f(x) = 2x-4, the transformed function is f(x) = -2x+4.
Therefore, the function rule for the function shown is -f(x).
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What’s 5 more than twice a number
Answer:
33 is the correct answer
Answer:
2x+5
Step-by-step explanation:
if the number is x
∴ 5 more than twice a number is
ll ll
V V
+5 *2
So, 2*x+5
What is the justification for the first step in proving the formula for factoring the sum of cubes? a3 b3 = (a b)(a2 â€"" ab b2) = a3 â€"" a2b ab2 a2b â€"" ab2 b3 distributive property commutative property definition of additive inverse definition of multiplicative inverse
The justification for the first step in proving the formula for factoring the sum of cubes [tex]a^3+b^3[/tex] is the distributive property.
Given the formula for sum of cubes [tex]a^3+b^3[/tex] = [tex](a+b)(a^2-ab+b^2)[/tex]
= [tex]a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]
In this step distributive property is utilized.
Distributive property is used for expanding the factors into the polynomial.
i.e., a(b+ c) = ab +ac
or, (a+ b)c = ac + bc
This is referred as the distributive property.
In the formula for [tex]a^3+b^3[/tex], (a+ b) is distributed over [tex](a^2-ab+b^2)[/tex].
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Answer:
a. Distributive
Step-by-step explanation:
took da test 100%
Write each number as a percent.
1.72
CCSS ARGUMENTS Write a two-column proof.
Given: BD bisects ∠B .
BD ⊥ AC
Prove: ∠A ≅ ∠C
∠A ≅ ∠C under the CPCT condition (coresponding parts of congurent triangles).
What accurately does the term "triangle congruency" mean?Two triangles are considered to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: BD bisects ∠B and BD ⊥ AC.
To prove: ∠A ≅ ∠C
First, prove that △ABD≅△BDC.
∠DBA ≅ ∠DBC = Given: BD bisects ∠B∠BDA ≅ ∠BDC = (90°) Given: BD ⊥ ACSo, △ABD≅△BDC under AA condition.
Then, ∠A ≅ ∠C under CPCT condition.Therefore, ∠A ≅ ∠C under the CPCT condition (coresponding parts of congurent triangles).
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