Answers
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
Related Questions
Determine the equation of the parabola whose graph is given below. Write your answer in General Form. A parabola on a coordinate plane.
Answers
The equation of parabola becomes y = -2/25(x-3)^2 + 4.
According to the statement
we have given a graph and from this graph we have to find the equation of parabola in the general form.
So,
we know that the equation of parabola in general form is
y = a(x-h)^2 +k - (1)
From the graph we have:
a point on the graph is (x,y) = (-2,2)
the vertex of the graph is (h,k) = (3,4)
Now, substitute these values in the equation number (1)
Then
y = a(x-h)^2 +k
2 = a(-2-3)^2 +4
2 = a(-5)^2 +4
2 = a(25) +4
25a = -2
a = -2/25.
Now put a = -2/25 and (h,k) = (3,4) in the equation(1).
Then
the equation of parabola becomes y = -2/25(x-3)^2 + 4
So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.
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The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(0) = g(0) and f(2) = g(2)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answers
The function equality that represents the point where f(x) = g(x) is; A: f(0) = g(0) and f(2) = g(2)
How to interpret Graphed Functions?From the question, the curved red line represents g(x) while the straight blue line represents f(x).
Now, the equality of functions f(x) = g(x) is represented as a common function between their curves. Thus, we will just need to find a common point for both. This is;
f(x) has points (0, 4) and (2, 0).
g(x) has points (0,4) and (2,0).
It is pertinent to note that both functions have the same y-value for x=0 and x = 2. Thus, we can say that;
f(2) = g(2) and f(0) = g(0)
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If the parent function is \root(3)(x), describe the translation of the function y=\root(3)(x+4)-3
Answers
The parent function moves 4 units right and 3 units down. This is a translation by the vector.
According to the question,
Transformation [tex]\sqrt[3]{x}[/tex] maps onto [tex]\sqrt[3]{x+4} -3[/tex] . Take f(x) = [tex]\sqrt[3]{x}[/tex] and f(x+4)=[tex]\sqrt[3]{x+4}[/tex].
f(x) = [tex]\sqrt[3]{x}[/tex]
f(x+4)=[tex]\sqrt[3]{x+4}[/tex]
f(x+4) - 3=[tex]\sqrt[3]{x+4}[/tex] - 3
Analyze the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive 'x' direction. f(x)-3 corresponds to a vertical translation 3 units in the negative 'y' direction.
Hence, the parent function moves 4 units right and 3 units down. This is a translation by the vector.
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PLS HELP IM STUCK PLS
Answers
Answer:
See below
Step-by-step explanation:
Slope, m of given line = - 1/2
perpendicular slope is = -1/m = -1 / (-1/2) = +2
Point (6,9) slope form of line
y -9 = 2(x-6) expand and simplify
y - 9 = 2x -12
y = 2x -3
Can someone help me on these problems and show work please !
Answers
Answer:
1. 3 terms; degree 5
2. 2 terms; degree 3
3. 9mn³ + 14mn²
4. 9a^4b^3
Step-by-step explanation:
Problems 1 - 2:
Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.
The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.
The degree of the polynomial is the same as the degree of the term with the highest degree.
1.
3 terms
degree 5
2.
2 terms
degree 3
Problems 3 - 4:
Combine like terms. Like terms have the same variables and exponents.
3.
6mn³ - mn² + 3mn³ + 15mn² =
= 6mn³ + 3mn³ - mn² + 15mn²
= 9mn³ + 14mn²
4.
a^4b^3 + 8a^4b^3 =
= 1a^4b^3 + 8a^4b^3
= 9a^4b^3
the length of a rectangle exceeds its width by 17 inches, and the area is 18 square inches. what are the length and width of the rectangle
Answers
The length and width of the rectangle are 18 in and 1 in, respectively.
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle can be found for the formula : b*h, where b = base and h =height.
For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=b*h
18=(W+17)*W
18=W²+17W
W²+17W-18=0
Solving this quadratic equation, you have:
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]
[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
w1=1 and w2= -18
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², see.
18=l*w
18=l*1
l=18 in
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what is the
area of
Rectangle with the length 3 XY
and width
14X2y
Answers
Answer: [tex]42x^3 y^2[/tex]
Step-by-step explanation:
[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]
If the width of a rectangle can be represented by x and the length by x + 10, write an expression that can be used to represent the area of the rectangle. Simplify the expression as much as possible.
Answers
Answer:
The expression for area is (x)(x+10).
Step-by-step explanation:
Area=(w)(l)
Area=(x)(x+10)
(Note: This expression can be expanded, but then it wouldn't be fully simplified)
Hope this helps!
Please help quickly I need the answer now please you’ll be brainleist
Answers
Answer:
B
Step-by-step explanation:
See the attached image.
The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
A. 0 = –4.9t2 + 19.6t + 24.5
B 0 = –4.9t2 + 24.5t + 19.6
C. 19.6 = –4.9t2 + 24.5t
D. 24.5 = –4.9t2 + 19.6t
Answers
Answer: 0=-4.9t²+19.6t+24.5
Step-by-step explanation:
[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]
A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
Answers
The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.
What is the net Change in latitude and longitude of the helicopter?The net change in latitude of the helicopter can be evaluated as follows;
x = |-6.20° - 22.27°| = |-28.47°|
x = 28.47°
The net change in longitude of the helicopter can be evaluated similarly as follows;
y = |106.80° - 114.15°| = |-7.35°|
x= 7.35°
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Please help me
Given the quadratic function, describe in words the transformations and then
provide a sketch of the graph.
y = − 1/²(x+4)² - 7
Answers
WILL MAKE BRAINLIEST!!Determine if two triangles are congruent if they are state the triangle congruence statement.
Answers
Answer:
Yes they are congruent by SSS criterion Explanation:AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion
A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39). which are the equations of the directrices? x = ± y = ± x = ± y = ±
Answers
The equation of directrix is D. y=± 432/13.
Definition of hyperbola -
A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant . A curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.1. The vertex i at (0, 36) and a focus at (0, 39), then you have:
a=36
a²=1296
2. The equation of directrix is:
y = a² =c
c = 39
y = 1296/39
y = 432/13
Therefore, the answer is the option D, which is: D. y=± 432/13
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The complete question is -
A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)
Which are the equations of the directrices ?
A. x= ±12/13
B. y=±12/13
C. x=±432/13
D. y=± 432/13
Answer: Correct
Step-by-step explanation:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Answers
Step-by-step explanation:
1. Not neccesarily true
2. Not necessarily true
3. True because angles in a triangle add to 180°
4. Not necessarily true
5. True because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. Not necessarily true
The statements that are true about the triangle are:
Option C: m∠P + m∠Q + m∠R = 180°
Option E: PT, QU, and RS intersect at the same point.
How to find the true statements of the triangle?1. m∠Q = m∠R: This is not true because there is no indication that the angles are equal.
2.The length of QU is half the length of RP: This is not true because there is no length given to show that measurement.
3. m∠P + m∠Q + m∠R = 180°:
This is true because the sum of angles in a triangle add to 180°
4. QU ≅ RS:
This is not true because we are not told that they are congruent
5. PT, QU, and RS intersect at the same point:
This is true because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. The sum of the lengths of QU and RS is equal to the length of PT: This is not true because we are not told that.
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A sales tax of P9,000 is added to a purchase of P120,000 worth of
jewelry. What is the rate of sales tax?
Answers
Answer:
Find the rate of sales tax
R= 9000/120000
=0.075
=7.5%
So, the rate is 7.5%
Angles Related to a Circle. Solve for X
Answers
The value of x is (d) 1
How to solve for x?The angle ABC is given as:
∠ABC = 43x
The line AB touches the tangent line BC at point B.
However, the line AB is not a radius.
This means that:
∠ABC < 90
So, we have
43x < 90
Divide by 43
x < 2.09
From the list of options, the number less than 2.09 is 1
Hence, the value of x is (d) 1
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explanation?
please help asap
Answers
Answer:
70 degrees = a
Step-by-step explanation:
Triangle= 180 degrees.
Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees
Which expression is equivalent to startfraction 10 x superscript 6 baseline y superscript 12 baseline over negative 5 x superscript negative 2 baseline y superscript negative 6 baseline endfraction? assume x not-equals 0, y not-equals 0.
Answers
[tex]3/ 5x^6*y^6[/tex] is the solution f the expression [tex](-9x^-1*y^-9) / (-15x^5*y^-3)[/tex]
Given expression:
(-9x^-1*y^-9) / (-15x^5*y^-3)
As we know, any number with negative power can be written in inverse form with positive power.
[tex]x^-a = 1/x^a[/tex]
Two number having same base their powers are added:
[tex]x^a + x^b = x^a+b[/tex]
[tex]= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)[/tex]
Hence the solution would be [tex]3 (5x^6 y^6)[/tex].
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Answer:
b
Step-by-step explanation:
If 2x + 3y = 194 and x = 28, what is the value of y?
Answers
Answer:
46
Step-by-step explanation:
For the value of y, substitute x = 28 into the equation.
2x + 3y = 194
2(28) + 3(y) = 194
56 + 3y = 194
3y = 194 - 56
3y = 138
dividing bothsides by 3
y = 46
Answer:
y = 46
Step-by-step explanation:
We want to find the value of y
2x+3y = 194
We are given the value of x
x=28
Substitute the value of x into the first equation
2(28)+3y = 194
56 + 3y = 194
Subtract 56 from each side
56+3y -56 = 194 -56
3y = 138
Divide each side by 3
3y/3 = 138/3
y =46
PLEASE HELP
If two lines are perpendicular, then the lines intersect to form four right angles that are 180° each.
False O True
Answers
Answer:
False
Step-by-step explanation:
[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees
The general term of a sequence is T(n)=n+2/n+3, find the value of T(1)*T(2)*T(3)*……….*T(100).
Answers
Answer:
T(1)=1+2(1)+3=6
T(2)=2+2(2)+3=9
T(3)=3+2(3)+3=12
T(100)=100+2(100)+3=303
What is the value of the rational expression
2x- 1
x+5
when x = 0?
Answers
Answer:
5
Step-by-step explanation
becasue 2x0=0 and 1x0=0
and when you add 5 to 0 you get five
How do I get started on the second part
Answers
The function to calculate the speed is S = 260.52/t.
How to illustrate the information?From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:
= 78 × 3.34
= 260.52km
The function to calculate the speed will be:
Speed = Distance/Time
S = 260.52/t
Complete question:
The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.
a. What is the total length of the race?
b. Write a function that can be used to model the race where the independent variable represent the average speed.
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Can someone help me please
Answers
Answer:
The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of the midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
The slope of a line segment with coordinates of the ends
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
Point D is the midpoint of a segment AB
A ( 4 , 12 )
B ( - 6 , - 8 )
( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )
D ( - 1 , 2 )
C ( 8 , - 6 )
[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]
18. In AABC, 44 is a right angle, and m4B 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The
diagram is not drawn to scale.
054 ft
17√3 ft
17√2 ft
017
Answers
Answer:
17√3
Step-by-step explanation:
In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.
17*√3 = 17√3
What is the volume, in cubic centimeters, of a cube whose side measures 4 centimeters ?
Fill in the blank by entering only a number as your answer.
Answers
The formula for the volume of a cube is-side length^3.
For your problem, side length=4, so the answer is 4^3=64
ANSWER: 64 CUBIC CENTIMETERS hope this helped you
(T-Tb)
In trapezoid LOVE, the length of the midsegment is 2x inches. If one
parallel side is x inches, what is the length of the other parallel side?
Answers
The length of the other parallel side is 3x
How to determine the other parallel side?The given parameters are:
Midsegment= 2x
One parallel side = x
The midsegment is calculated as:
Midsegment = 0.5 * (sum of parallel sides)
So, we have
2x = 0.5 *(x + Other side)
Divide by 0.5
4x = x + Other side
Evaluate the like terms
Other side = 3x
Hence, the length of the other parallel side is 3x
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Giving away brainly for help ASAP
Answers
Answer:
[tex]g(f(x))=25x^2-15x-7[/tex]
domain: (-∞,∞)
Step-by-step explanation:
g of f means plug the function f(x) in to x in the function g(x)
[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]
since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013
Answers
A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
How to determine the Journalist statement about this piece of information after analyzing the data?From the question, we have the following highlights:
Year = 2008 to 2013 (this represents the domain)Owner's claim: Production increased at an exponential rateFrom the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph
This is so because the points on the graph are connected by a straight line.
Linear graphs have constant rate
Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
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Complete question
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?