The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
How to determine the equation of the line?The complete question is added as an attachment
The points on the line are given as:
(-1, 1) and (0, -3)
Start by calculating the slope of the line using
m = (y2 - y1)/(x2 - x1)
The slope of the perpendicular line is
m2 = -(x2 - x1)/(y2 - y1)
So, we have:
m2 = -(0 + 1)/(-3 - 1)
This gives:
m2 = 1/4
The equation of the line is then calculated as
y - y1 = m(x - x1)
This gives
y + 3 = 1/4(x + 4)
Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
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mangleR = 120° and mangleS = 100°. Find mangleT. The diagram is not drawn to scale.
Which of the following functions has an initial value of -1/2 and a rate of change of 0?
A.
2
x
B. y=−12x
y
=
−
1
2
x
C. y=−12x
y
=
−
1
2
x
D. y=−12
The function that has the given initial value and rate of change is: D. y = -1/2.
What is the Initial Value and Rate of Change of a Function?A function is given as, y = mx + b, where, m is the rate of change, and b, which is a constant is the initial value.
Given the following:
b = -1/2
m = 0
Plug in the values into y = mx + b
y = 0(x) + (-1/2)
y = -1/2
Therefore, the function is: D. y = -1/2.
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Identify the compositions performed on ΔXYZ to map onto ΔX″Y″Z″.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
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Resuelve los siguientes ejercicios:
Hallar la ecuación de la circunferencia:
a) Centro (2,-1) y radio 4
b) Centro C (1,3) y que pasa por el punto P (4, 6)
3. Hallar la ecuación de la parábola, las coordenadas de su foco y la longitud de su lado recto, si el vértice es el origen y pasa por el punto P:
a) Eje focal coincidente con el eje coordenado en x, P(2,4)
b) Eje focal coincidente con el eje coordenado en, P (6,3)
4. Hallar el foco, la ecuación de la directriz y la longitud del lado recto de las siguientes parábolas.
a) 4 x2 = 32y
b) 2y2 = -3x
5. Dadas las ecuaciones de las elipses, hallar las longitudes del semieje mayor y semieje menor, las coordenadas de los focos, los vértices y la longitud del lado recto.
a) 81 x2 + 144 y2 = 11664
b) 36x2+25y2 = 3600
Por restricciones de longitud no es posible resumir las respuestas asociadas a esta pregunta, invitamos cordialmente a leer la explicación para mayores detalles sobre el análisis de secciones cónicas.
¿Cómo analizar ecuaciones de secciones cónicas?
Según la geometría analítica, existen cinco tipos de secciones cónicas: (i) Circunferencia, (ii) Parábola, (iii) Elipse, (iv) Hipérbola, (v) Recta. 2) a) La ecuación estándar de la circunferencia se caracteriza con el centro (h, k) y la longitud del radio (r):
(x - h)² + (y - k)² = r²
(x - 2)² + (y + 1)² = 4²
b) La longitud del radio de la circunferencia se obtiene por el teorema de Pitágoras sobre la longitud del segmento CP:
r = √[(4 - 1)² + (6 - 3)²]
r = √(3² + 3²)
r = 3√2
(x - 1)² + (y - 3)² = 18
3) a) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:
4 · p · x = y²
Donde p es la distancia entre el foco y el vértice.
Si tenemos que (x, y) = (2, 4), entonces la ecuación de la parábola es:
4 · p · 2 = 4²
p = 2
8 · x = y²
Las coordenadas del foco de la parábola son de la forma (x, y) = (h + p, k):
F(x, y) = (2, 0)
Ahora se determinan los extremos del lado recto: (x = 2)
8 · 2 = y²
y = ± 4
Los extremos del lado recto son (2, 4) y (2, - 4), cuya longitud de segmento es 8 unidades.
b) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:
4 · p · x = y²
Si tenemos que (x, y) = (6, 3), entonces la ecuación de la parábola es:
4 · p · 6 = 3²
p = 8 / 3
(32 / 3) · x = y²
Las coordenadas del foco son F(x, y) = (8 / 3, 0).
Ahora se determinan los extremos del lado recto: (x = 6)
(32 / 3) · 6 = y²
y = ± 8
Los extremos del lado recto son (6, 8) y (- 6, - 8), cuya longitud de segmento es 16 unidades.
4) a) Tenemos una ecuación estándar de la forma 4 · p · y = x². A continuación, hallamos todas las variables requeridas:
x² = 8 · y
p = 2
Directriz: y = - 2, Foco: F(x, y) = (0, 2), Longitud del lado recto: 4
b) Tenemos una ecuación estándar de la forma 4 · p · x = y². A continuación, hallamos todas las variables requeridas:
y² = - (3 / 2) · x
p = - 3 / 8
Directriz: x = 3 / 2, Foco: F(x, y) = (- 3 / 2, 0), Longitud del lado recto: 3.
5) En esta parte debemos manipular algebraicamente las ecuaciones hasta su forma estándar para determinar los datos requeridos de cada caso. La ecuación estándar de la elipse tiene el siguiente problema:
(x - h)² / a² + (y - k)² / b² = 1
Donde:
(h, k) - Centro de la elipse.a, b - Longitudes de los semiejes.a) 81 · x² + 144 · y² = 11664
x² / 144 + y² / 81 = 1
x² / 12² + y² / 9² = 1
Longitud del semieje mayor: 12
Longitud del semieje menor: 9
c = √(12² - 9²)
c ≈ 7.937
Coordenadas de los focos: F₁ (x, y) = (- 7.937, 0), F₂ (x, y) = (7.937, 0)
Vértices: V₁ (x, y) = (- 12, 0), V₂ (x, y) = (12, 0)
Longitud del lado recto
144 · y² = 11664 - 81 · x²
y² = (11664 - 81 · x²) / 144
y = ± (1 / 12) · √(11664 - 81 · x²)
y = ± (1 / 12) · √(11664 - 81 · 7.937²)
y = ± 6.750
La longitud del lado recto es 13.5.
b) 36 · x² + 25 · y² = 3600
x² / 10² + y² / 12² = 1
Longitud del semieje mayor: 12
Longitud del semieje menor: 10
c = √(12² - 10²)
c ≈ 6.633
Coordenadas de los focos: F₁ (x, y) = (0, - 6.637), F₂ (x, y) = (0, 6.637)
Vértices: V₁ (x, y) = (0, - 12), V₂ (x, y) = (0, 12)
Longitud del lado recto
36 · x² = 3600 - 25 · y²
x² = 100 - (25 / 36) · y²
x = √[100 - (25 / 36) · y²]
x = √[100 - (25 / 36) · 6.637²]
x = ± 8.331
La longitud del lado recto es 16.662.
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helpppp meeeeee
Which expression represents the following statement? Add 8 to 6 times the quotient of 21 and 3.
6 x (21 ÷ 3) + 8
6 + 8 − (21 ÷ 3)
21 ÷ 3 − (8 + 6)
6 x (21 + 3) + 8
Answer:
(a) 6 x (21 ÷ 3) + 8
Step-by-step explanation:
The first step in translating English to math is to understand the English.
Parsing itThe quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...
6×(21÷3)
When 8 is added to this, it becomes ...
6 × (21 ÷ 3) + 8
I need help determining how many roots
By graphing the polynomial, we conclude that there is only one real root, so the correct option is A.
How many roots has the given polynomial?
We have the polynomial:
[tex]y = -3x^2 + 12x - 12[/tex]
To see how many real roots this polynomial has, we can graph it and see how many times the graph intercepts the x-axis.
The graph can be seen below:
There we can see that there is only one intercept, so there is only one real root.
So the correct option is A.
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What’s the volume of a rectangle solid with the given dimensions: length 20, width 23, height 26
The volume of the rectangular solid is: 11,960 units³.
How to Find the Volume of a Rectangular Solid?The formula to find the volume of a rectangular solid is: (length)(width)(height).
Given the dimensions as:
Length = 20 unitsWidth = 23 unitsHeight = 26 unitsVolume = (20)(23)(26)
Volume of the rectangular solid = 11,960 units³.
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Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?
because both triangles appear to be equilateral
because∠MNL and ∠ONP are congruent angles
because one pair of congruent corresponding angles is sufficient to determine similar triangles
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
The information is enough because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
What are Similar Triangles?Similar triangles can be formed during dilation. All corresponding angles of similar triangles are usually congruent to each other.
From the image given, the using rotation about point N and then dilation by a scale factor will make both triangles similar. Thus, with the given information, we can determine both triangles are similar because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
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Answer:
C
Step-by-step explanation:
Took the test
A new plasma TV was marked down 20%. The new sale price of the TV was $380. What is the TV’s regular selling price?
x=regular selling price
X×80/100=380
= X×8/10=380
= 8X=380×10=3800
X=3800/8
X=475
the regular selling price is 475
Before the 20% discount, the TV's regular selling price was $475 as per the concept of percentage.
Let's denote the regular selling price of the plasma TV as "x". When the TV was marked down by 20%, the sale price became $380.
To find the regular selling price, we can set up an equation using the information given:
Sale Price = Regular Selling Price - (Discount Percentage × Regular Selling Price)
$380 = x - (0.20x)
Now, let's solve for "x" (the regular selling price):
$380 = x - 0.20x
$380 = 0.80x
To isolate "x," we divide both sides of the equation by 0.80:
x = $380 / 0.80
x = $475
The regular selling price of the plasma TV is $475.
Therefore, before the 20% discount, the TV's regular selling price was $475. After the discount, the sale price was reduced to $380, which is 20% less than the regular price.
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look at the pictures
The key feature that the function of f(x) and g(x) has in common is the domain.
What is the domain and range of a function?The domain of a function is the set of input or argument values for which the function is valid and well defined. The range is the set of the dependent variable for which a function is defined.
From the given information, we are to find the domain, range, x-intercept, and, y-intercept of the given equation:
[tex]\mathbf{f(x) = -4^x+5}[/tex]
[tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]
For [tex]\mathbf{f(x) = -4^x+5}[/tex];
The domain of a function [tex]\mathbf{-4^x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.
The range f(x) < 5. The x-intercepts, when y is zero = [tex]\mathbf{(\dfrac{In(5)}{2In(2)},0)}[/tex]The y-intercepts; when x is zero = (0,4)For [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]
The domain of a function [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.
The range -∞ < f(x) < ∞. The x-intercepts, when y is zero = (-2.939, 0)The y-intercepts; when x is zero = (0,5)Learn more about the domain and range of a function here;
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You get a raise of 3.5% each year.
a. What is the approximate doubling time of your salary?
b. If you are currently 25 years old and are making $40,000 per year, use the approximate doubling time to find your annual salary when you retire at the age of 65.
Using an exponential function, it is found that:
a) The doubling time of the salary is of approximately 20 years.
b) The salary will be of $160,000.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The growth rate for this problem is:
r = 0.035.
The doubling time is t for which A(t) = 2A(0), hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]2A(0) = A(0)(1.035)^t[/tex]
[tex](1.035)^t = 2[/tex]
[tex]\log{(1.035)^t} = \log{2}[/tex]
[tex]t\log{1.035} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.035}}[/tex]
t = 20 years.
You retire in 40 years, which is 2 doubling periods, hence the salary will be of:
40000 x 2 x 2 = $160,000.
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Dave leaves his office in Padelford Hall on his way to teach in Gould Hall. Below are several different scenarios. Take distance units to be “feet” and time units to be “minutes.” Assume Dave’s path to Gould Hall is along a straight line which is 2400 feet long.
I. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 10 minutes later.
II. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the halfway point. Then he gets confused and stops for 1 minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall.
III. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for 1 minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall.
g. Using all three scenarios, represent each scenario as an algebraic function.
See below for the algebraic expressions of the scenarios.
How to represent the scenarios?The given parameters are:
Distance = 2400 feetUnit of time = MinutesScenario 1
Represent the speed with x.
So, we have:
Speed = Distance/Time
The time is given as:
Time = 10 minutes
Since he did not stop at all;
The speed is
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 1.
Scenario 2
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at the same initial speed
So, the total time it 13 minutes
The speed is represented as:
x = 2400/13
Multiply both sides by 13
13x = 2400
The above expression represents the scenario 2.
Scenario 3
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at twice the initial speed
So, the total time is
t = 6 + 1 + 1/2 * 6 minutes
t = 10 minutes
The speed is represented as:
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 3.
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The function f(x) = 300(0.5)x/100 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after Round to the nearest whole number.
The amount of the radioactive material in the vault after 140 years is 210 pounds
How to determine the amountWe have that the function is given as a model;
f(x) = 300(0.5)x/100
Where
x = number of years of the vault = 140 yearsf(x) is the amount in poundsLet's substitute the value of 'x' in the model
f(x) = 300(0.5)x/100
[tex]f(x) = \frac{300(0.5) * 140}{100}[/tex]
[tex]f(x) =\frac{21000}{100}[/tex]
f(140) = 210 pounds
This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.
Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds
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Find the sum of the arithmetic series 8 +13 +...+ 58.
a) 726
Ob) 1914
Oc) 330
d) 363
Answer:
363 (d)
Step-by-step explanation:
Sum = (a1+an)(n)/2
n = (an-a1)/d +1 = 11
Plug into the sum formula.
Sum = 363
The prep club and honor society are joining forces
Given that the inequalities and that
x ⇒ pep club donations
y ⇒ represent donations raised by the honor society
The inequality is represented by x + y≥ 500
The solution for this is the shaded area above the solid line.
Given x ≥ 100, this is also indicated by the shaded region to the right
What does point (300, 100) represent? is it a viable Solution? why?The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.
The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.
To proof the above,
Let x = 300; and y = 100
Plugin in both values in the inequalities we have:
300 + 100 [tex]\ngeq[/tex] 500
400 [tex]\ngeq[/tex] 500 ; Hence it is NOT true; also
300 [tex]\ngeq[/tex] 500.
What does (500, 200) represent? Is it a viable Solution? why?The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.
The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.
To proof the above,
Let x = 500; and y = 200
Plugin in both values in the inequalities we have:
500 + 200 ≥ 500
700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.
Conclusion:
The point (500, 200) is a viable solution.
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Explain how to draw a line segments that measures 2 7/16 inches.
The line segment which represents 2 7/16 inches should first be drawn with the use of a ruler.
What is a Ruler?This is referred to an instrument which is used to measure distances between points or draw straight lines and also usually graduated in inches.
On the inches graduation, the zero mark should be located and the 1/16 inch which is found before the half-inch mark between 2 and 3 inches. When this is done, a line should be drawn to meet both points which will therefore measure 2 7/16 inches long.
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Planes A and B intersect.
n
772
W
k
Mark this and return
V
19
Z
X
2
Which describes the intersection of line m and line nº
O point W
point X
point Y
O point Z
The point that describes the intersection of line m and line n is; Point W
How to interpret Intersection of Planes?
Intersection of the two lines is defined as the point where the two lines cross or meet each other.
It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.
From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.
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A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3840 MB. How many downloads of the standard version were there?
Step-by-step explanation:
s = number of standard downloads
2s = number of high-quality downloads
2.8s + 4.6(2s) = 2760
2.8s + 9.2s = 2760
12s = 2760
s = 230
The standard version was downloaded 230 times and the high-quality version was downloaded 460 times.
Nan is 20 year old. In 8 years,she will be twice as old as Clarisse.how old is clarisse now?
Answer:
6
Step-by-step explanation:
The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.
n this equation, one-fourth is added to the variable y.
y+14=34
What is the value of y?
The value of y is = -------------
Answer:
I think its 19.75
Which represents an exterior angle of triangle ABF?
∠BAD
∠AFE
∠CAD
∠CAB
The angle that represents an exterior angle of the given triangle is: D. ∠CAB.
What is an Exterior Angle of a Triangle?An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.
In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.
Therefore, the answer is: D. ∠CAB.
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The graphs of f(x) = 5* and its translation, g(x), are
shown on the graph.
30 1x
30 25 20 15 10 f
goxx)
40
f(x)
-6-5-4-3-2-15-
(1,5)
(0
(2,25)
(2, 15)
2 3 4 5
(1.-5)
-10-0.9)
-15-
-20
-25
30
X
What is the equation of g(x)?
Og(x) = 5x-9
Og(x) = 5x-10
Og(x) = 5-9
Og(x) = 5-10
g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:
[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]
Which is the equation of the translation?Here we know that:
[tex]f(x) = 5^x[/tex]
And we want to find the equation for g(x), which is a translation of f(x).
If you look at the graph of f(x), you can see that it passes through:
(0, 1), (1, 5), (2, 25), etc.
And the graph of g(x) passes through:
(0, -9), (1, -5), (2, 15)
So in each point, the y-component is 10 units smaller than the correspondent for f(x).
Then g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:
[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]
So the correct option is the last one.
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What is the ratio between 40,000 and 200?
The ratio between 40,000 and 200 is 200 : 1
How to determine the ratio?The numbers are given as:
40,000 and 200
Express as ratio
Ratio = 40000 : 200
Divide each number by 200
Ratio = 200 : 1
Hence, the ratio between 40,000 and 200 is 200 : 1
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Tell wether 3 is a solution of each inequality
x-7> -5; x = 3
-3x< - 12.5 ; x=3
Write an equation for this word
sentence: one fifth of a number
equals 16.
Answer: x / 5 = 16
x = 80
Someone please help me with this geometry question!
Answer: SAS
Step-by-step explanation:
There are two pairs of congruent angles and the pair of angles formed by these sides are congruent.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
In the given figure, one angle and two adjacent sides of Triangle AFB is equal to corresponding angle and sides of the Triangle DFC.
So, we can conclude that,
Triangle AFB and Triangle DFC are congruent by :
SAS congruency criteria[tex] \qquad \large \sf {Conclusion} : [/tex]
A. SASEasy points because I got points to blow,
Answer:
Did you know that the first person convicted of speeding was going eight mph.
Step-by-step explanation:
A teacher designs a test so that 93% of students who study will pass and 9% of students who don't study will pass. 88%
of students study for a test. What is the probability that a randomly selected student passes?
A. 1.057
B. 0.833
C. 0.084
D. 0
E. 0.829
Answer:
Step-by-step explanation:
First find the percentage of the ones that pass that study
.93 *(88)=88.84%
next find the ones that pass that did not study
.09*(100-88)=1.08
sum these to get the total passing percentage
88.84+1.08=82.92%
The probability is 82.9 per 100 or .8292 for student
E is the answer
Multiply –8m(–6m – 7).
–14m2 – 15m
48m2 + 56m
–14m – 15
48m + 56
Answer: 48m2 + 56m
Step-by-step explanation:
Answer:
Answer B
Step-by-step explanation:
Es LOGICA PROPOSICIONAL, me pueden ayudar porfavor?
[tex]\begin{array}{c|c|c|c} p & q & \neg q & p \land \neg q \\ T & T & F & F \\ T & F & T & T \\ F & T & F & F \\ F & F & T & F \end{array}[/tex]
[tex]\begin{array}{c|c|c|c} t & s & \neg t & \neg t \implies s \\ T & T & F & T \\ T & F & F & T \\ F & T & T & T \\ F & F & T & F \end{array}[/tex]
[tex]\begin{array}{c|c|c}p\land \neg q & \neg t \implies s & (p \land \neg q) \implies (\neg t \implies s) \\T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array}[/tex]
The given logical statement is false when [tex]p\land\neg q[/tex] and [tex]\neg t\implies s[/tex] are true and false, respectively.
[tex]p\land\neq g[/tex] is true when [tex]p[/tex] is true and [tex]q[/tex] is false[tex]\neg t \implies s[/tex] is false when both [tex]t[/tex] and [tex]s[/tex] are false