At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2
To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).
Since the x-intercept is 3/4x, the equation of the tangent line is
y - y_p = (3/4)(x - x_p).
We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.
y - 16
= (3/4)(x - 1).
This equation is the equation of the curve.
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Prove that every point on the perpendicular bisestor of a segment is equidistant from the endpoint of segment​.
Every point on the perpendicular bisector of a segment is equidistant from the endpoint is hence proved
The line segment AB and let MN is the perpendicular bisector of AB line segment.
we prove the required result by congruence of triangles.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure
From the figure,
Let P be any point on the perpendicular bisector MN. Join A to P and B to P.
To show AP=BP
In ΔANP and ΔBNP
PN=PN {common side in both triangles }
∠PNA=PNB=90°{ MN is ⊥ bisector of AB}
AN=NB {N is mid point}
By SAS rule of congruent ΔANP≅BNP
By CPCT (corresponding Parts of congruent triangles)
AP=BP
But P is point on MN
Therefore, every point on the perpendicular bisector of line segment AB is equidistant from the segments endpoints.
Hence Proved.
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A rectangular closet is 4 feet long. It is 3 times as wide as it is long.
Label the diagram with the dimensions of the closet.
12
ft
4
ft
4
ft
4
ft
4
ft
Great job!
Find the perimeter of the closet.
12 ft
4 ft
4 ft
4 ft
4 ft
The perimeter of the closet is
feet.
The dimensions of the closet are 4 feet long and 12 feet wide and the perimeter is 32 feet
What is the perimeter of a rectangle?The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides.
P=2(l+w) where l=length and w = width
Given here rectangular closet is 4 feet long and It is 3 times as wide as it is long. Thus its width would be 12 feet
Now perimeter of the closet using the formula above we get
P = 2(4+12)
= 32 feet
Hence the perimeter is equal to 32 feet.
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b) Without a calculator, evaluate (0.1)² = (0.1)4
Answer:
false
Step-by-step explanation:
The left side equals 0.01
The right side equals 0.4
The two sides are not equal. This is a false equation.
Answer:0.01=0.0001
Step-by-step explanation:
please help with this question
Answer: the answer should be C :)
Step-by-step explanation:
the slope (x) is -3/4 and the y-intercept is -2
Damian works after school. each day he earns a set amount, plus an hourly wage. the function f(x) = 12x + 10 models the amount he earns each day for working x hours. how much does damian earn on friday if he works for 2.75 hours?
Answer:
$43
Step-by-step explanation:
[tex]f(2.75) = 12(2.75) + 10 [/tex]
[tex] f(2.75) = 33 + 10 = 43[/tex]
designs for their
In popular online role playing game, players can create detailed
character's "costumes," or appearance. Abigail sets up a website where players can
buy and sell
these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
146 visitors purchased no costume.
230 visitors purchased exactly one costume.
A
31 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a decimal to the nearest hundredth.
The probability that the next person will purchase exactly one costume is 0.57.
what is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
146 visitors purchased no costume.
230 visitors purchased exactly one costume.
31 visitors purchased more than one costume.
So, the total number of customers are,
146 + 230 + 31 = 407
The total visitors purchased exactly one costume are 230.
So,
P(Purchase exactly one costume) = 230 / 407 = 0.5651 ≈ 0.57
Hence, the probability that the next person will purchase exactly one costume is 0.57.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is the distance between points F and G?
Tamba jut received a bonu which increaed hi dipoable income by $860. If Tamba' marginal propenity to conume (mpc) i 0. 75, hi conumption rie by _______
The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645
The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.
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Evaluate:
10 Σn=1 8(1/4) n -1= [?]
Mixed Number Form is 102184532768.
Evaluate:10 Σn=1 8(1/4) n -1= [?]10∑n=18(14)n−1
The sum of a finite geometric series can be found using the formula a(1−rn1−r)
where a is the first term and r
is the ratio between successive terms.
Find the ratio of successive terms by plugging into the formula r=an+1an
and simplifying.
r=14
Find the first term in the series by substituting in the lower bound and simplifying.
a=8
Substitute the values of the ratio, first term, and number of terms into the sum formula.
81−(14)101−14
Simplify.
34952532768
The result can be shown in multiple forms.
Exact Form:
34952532768
Decimal Form:
10.66665649…
Mixed Number Form:
102184532768
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Find the slope of the line y=
10/19x+15.
Write your answer as an integer or as a simplified proper or improper fraction.
Answer:
10/19
Step-by-step explanation:
the slope of the line is the term that multiplies x
Answer: 10/19 is the slope
what is the answer to 3^4 + 18 ÷ 3 +2
Answer:
89
Step-by-step explanation:
[tex] {3}^{4} + \frac{18}{3} + 2 \\ = 82[/tex]
o Answer:
It's 89 and I didnt mean to reaspond to this question so report it
Find the value of x and the two equations
× is 7
(7×+5) is 54
(5×+19) is 59
FILL IN THE BLANK. _________ are the characteristics of the individuals of the population being studied.
Answer:
Variables
Step-by-step explanation:
Variables are the characteristics of the individuals of the population being studied.
Which of the following is an example of rational function?
1.f(x)=3x²+1 over x-1
2.x over 3 = 8 over 3
3.1 over 3x-1 +3<0
An example of a rational function is the first equation given, f(x)=3x²+1 over x-1.
A rational function is a type of function that can be expressed as the ratio of two polynomials. In this equation, the numerator is a polynomial of degree 2 (3x²+1), and the denominator is a polynomial of degree 1
(x-1).
The second equation given, x over 3 = 8 over 3, is not an example of a rational function. This equation is a rational expression, which is an expression that is the ratio of two polynomials, but it is not a function because it does not map a single input to a single output.
The third equation given, 1 over 3x-1 +3<0, is not an example of a rational function either. This equation is an inequality, not a function, and it does not have a ratio of two polynomials.
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help pls i don’t understand this cause my teacher can’t teach
Answer:
A
Step-by-step explanation:
cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]
if the probability that a baby born in a certain hospital will speak in the next day is , what is the probability that at least babies out of a cluster of babies will speak tomorrow?
The probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow is 47/128.
The probability that less than 2 babies will speak is
5C0 * (0.25)^0 * (0.75)^5 + 5C1 * (0.25)^1 * (0.75)^4
= (0.75)^5 + 5 * 0.25 * (0.75)^4
(0.75)^5+5*0.25*(0.75)^4 = 81/128
Therefore,
probability that 2 or more will speak is
= 1- 81/128 = 47/128
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability display style q=1-pq=1-p).
This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.
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Help me? Care to explain also?
*Gives Brainliest for best ans easy to read answer!*
Answer:
B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
if you divide 7 by 12 you will get a decimal and a non terminating 3
What is ALWAYS true about the
coordinates of x-intercepts?
the x-value will be 0
the x-value will be equal to the y-value
the y-value will be 0
Answer:
The y-value will be 0
Step-by-step explanation:
The x-value will be 0 when we find the y-intercept
the x-value will be equal to the y-value is only at origin (0,0)
The answer is the y-value will be 0
Mike has a box with 5 white marble, 3 green marble and 2 blue marble. he picks 2 marbles from the box. what is the probability that he will get two green marbles?
Answer:
1/15
Step-by-step explanation:
3/10 x 2/9
At a birthday party, Samuel ate
Complete the statement:
1
10
of the birthday cake.
If the cake can be represented as 1 =
10
10
that means we can find out how much cake is left by taking
and then subtracting the amount Samuel ate.
The expression [DROP DOWN 1] represents this situation.
10
10
If the cake can be represented as 1 = 10/10, that means we can find out how much cake is left by taking and then subtracting the amount Samuel ate. The expression [1 - 1/10] represents this situation.
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
Cake = 1 or 10/10
Samuel's bite = 1/10
The amount remaining is calculated as
Amount remaining = Cake - Samuel's bite
Substitute the known values in the above equation, so, we have the following representation
Amount remaining = 1 - 1/10
The above represents the required expression
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how much work is done raising an 8 lb mass to a height of 18 ft above the ground? (use decimal notation. give your answer as an exact number.)
Therefore, the work done in this problem comes out to be 144 ft pound.
Where is the work done?The work a force does is calculated as the product of the object's displacement and the components of the applied force of the object in the displacement direction. Pushing a block with some force and accelerating the body results in work being completed.
Here,
Given : an 8 lb mass
a height = 18ft
So, we find the work done
Using formula
=> Work done = m*g*h
=> Work done = weight * height
=> Work done = 8*18
=> Work done=144 ft pound
Therefore, the work done in this problem comes out to be 144 ft pound.
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What is the Pythagorean theorem? How do you use it to find the length of a missing side in a right triangle? Give an example and show your work.
The sum of squares of two sides of a triangle is equal to another side of a triangle is called the Pythagorean theorem.
It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
c^2=a^2+b^2--------(1)
Where a,b, and c are sides of a triangle.
To measure the length of the missing side in a right triangle using the Pythagorean theorem:
c^2=a^2+b^2
By using this formula we can find the length of a missing side.
To understand more we have to solve an example:
let A, B, and C are points of a triangle AB, BC, and CA are the sides of the triangle.
Consider BC=3cm CA=4cm AB=?
Use equation(1) to find the length of AB
AB^2=BC^2+CA^2
AB^2=3^2+4^2
AB^2=9+16=25
AB=5cm
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△ABC ha vertice A(1, 3), B(2, 5), and C(5, 3). What are the coordinate of B′ after the tranformation (x, y) ⟶ (–y, x), then tranlation 1 unit right and 4 unit up? help me out pl
On translating n 1 unit right and 4 unit up , we get the coordinates of B as B'( 3, 9).
The given triangle ABC has the following vertices A(1, 3), B(2, 5), and C(5, 3).
We will apply the translation rule on the following triangle,
T⟨1, 4⟩
A(1, 3)
A( 1+ 1 , 3+ 4 ) = A( 2, 7)
B(2, 5)
B( 2+ 1 , 5+ 4 ) = B( 3, 9)
C(5, 3)
( 5+ 1 , 3+ 4 ) = C ( 6, 7)
Therefore , the coordinates of B' is B'( 3, 9) as calculated after using the rule.
Translation rule is a rule in mathematics which moves a shape left , right , up or down. The newly formed shape is the same as before , just their direction gets changed.
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Given the equation
2x² = 12x - 5
enter the values of a, b, and c, where a is a positive integer.
The values of a= 2, b= -12 and c= 5.
What is Quadratic Equation?Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.
Quadratic equations are another name for it.
The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
Given:
Equation: 2x² = 12x - 5
Rewriting the equation
2x² - 12x + 5 =0
We know that the standard form of Quadratic Equation is
ax² + bx + c = 0
where a, b, and c are integers and a ≠ 0.
Now, Comparing the standard equation with Given equation we get
a= 2, b= -12, c= 5
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In triangle xyz, m∠y = 45.43° and m∠z = 38.7°. determine the measure of the exterior angle to ∠x. 44.57° 51.3° 75.75° 84.13°
Answer:
[tex]84.13^{\circ}[/tex]
Step-by-step explanation:
By the exterior angle theorem, the answer is [tex]m\angle y+m\angle z=84.13^{\circ}[/tex].
Answer:
Step-by-step explanation:
USE THE EXTERIOR ANGLE THEROME!
FIRST
THE FOMULA
a+b=c
y+z=x
now we have to add y and z
45.43 + 38.7
which gives us 84.13!
The table shows a school district's enrollment
for two successive years. Write a linear function
using the data (with x representing the year
number), and then use the model to predict the
enrollment in Year 4.
Year 1 - 8295
Year2 -8072
to get the equation of any straight line, we simply need two points off of it, let's use those two in the table
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{Year}{x}&\stackrel{students}{y}\\ \cline{1-2} 1&8295\\ 2&8072\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{8295})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8072}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8072}-\stackrel{y1}{8295}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ -223 }{ 1 } \implies - 223[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8295}=\stackrel{m}{- 223}(x-\stackrel{x_1}{1}) \\\\\\ y-8295=-223x+223\implies {\Large \begin{array}{llll} y=-223x+8518 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{for year 4, x = 4}}{y=-223(4)+8518} \implies y=7626~students[/tex]
Am I correct? Since the measure of the triangle is always 18. So, I added 117+ 33 which gave me 150. Next, I subtracted 150 from 150 from one side. Then, I subtracted 180 from 150 which gave me 33.
The measure of the angle ∠ACD will be 150°. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The internal angles ∠A is 33° and ∠B is 117°.
Then the measure of the internal angle ∠C is given as,
∠A + ∠B + ∠C = 180°
33° + 117° + ∠C = 180°
∠C = 30°
The angle ∠C and angle ∠ACD are supplementary angles. Then we have
∠C + ∠ACD = 180°
30° + ∠ACD = 180°
∠ACD = 150°
The measure of the angle ∠ACD will be 150°. Then the correct option is D.
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Use the given information to prove that angle 8 is congruent to angle 1. Use two-column proof.
By using the properties of angle, it can be proved that [tex]\angle 8 \cong \angle 1[/tex]
What is angle?
An angle is a figure formed by two straight lines that intersect each other. It is a measure of the amount of rotation between two lines or planes, typically measured in degrees or radians. Angles are used in mathematics to describe relationships between lines, shapes and objects, and they are also used in everyday life to measure and construct objects. Angles are an important part of geometry and trigonometry, and they are also used in physics, engineering, and other sciences.
[tex]\angle 8 \cong \angle 5[/tex] Vertically Opposite angle
[tex]\angle 5 \cong \angle 1[/tex] Corresponding angle
[tex]\angle 8 \cong \angle 1[/tex] Transitivity property of congruency
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HELP ME PLEASE ITS DUE AT 8 (50 POINTS)
Jamir bought p pencils that cost $0.10 each and F folders that cost $.35 each. A 8.75% sales tax will be applied to the total cost.
PART ONE:
Which expression repersents the total amount Jamir paid,including tax? Write the letter of the correct answer on the line below.
a) 0.0875 (p + f) + 0.0875 (0.10p+0.35f)
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
c) 0.35(0.0875f) + 0.10(0.0875p)
d) 0.35(1.0875f) + 0.10(1.0875f)
Answer=
PART B
Explain why each of the other answers are worng.
LAST PART
Jamir purchased a dozen pencils and 8 folders. How much did he spend in all,after all tax was applied? Show your work please
Answer$=
Answer:
b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)
first is Jamir total cost + the sales tax of 0.0875 of the total cost
a. this is wrong because both is the sales tax only, theres no total cost include
c. wrong because its just also sales tax only
d. wrong because the total cost must only multiplied by the sales tax
PART B
12(0.10) + 8(0.35)
= 1.2 + 2.8
= $4 as the total cost
4(1.035)
= $4.14 as after tax bill
CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
please help me with this question
many thanks
Answer:
111 girls
Step-by-step explanation:
You have 924 people classified as 383 men, 356 women, and the remainder children. 2/5 of the children are boys, and you want to know the number of girls.
GirlsThe number of children is ...
924 -383 -356 = 185
The 3/5 of children that are not boys are girls, so ...
girls = 3/5(185) = 111
There are 111 girls in the theater.