Answer:
Your answer is 56.
Step-by-step explanation:
To solve this problem, we simply need to plug in the given numbers into the expression.
If we do this, we get the following:
u + xy
2 + (9*6)
Using PEMDAS, we know that we have to perform the multiplication in this problem before the addition. Thus the first step in simplification is multiplying 9 and 6 together. If we do this, we get:
2 + 54
Next, we simply add together the two remaining terms.
54 + 2 = 56
Therefore, your answer is 56, the first option.
Hope this helps!
1. The equation y=x^2-9x+20 models the roller coasters path over time. The variable y represents height (in feet) above or below the platform. At y=0, the roller coaster is even with the platform. The variable x represent the amount of time (in seconds) since the ride began.
Part 1: write the equation in factored form.
Part 2: find the vertex of the parabola. Hint: to find the x-value of the vertex, take the average of the x-values of the x-intercepts of use the first part of the quadratic Formula (x=-b)
——
2a
Part 3: what is the y-intercept? Use the equation y=x^2-9x+20
Part 4: Sketch the graph of y=x^2-9x+20. Identify the vertex and x- and y-intercepts on your sketch
Part5: use the graph to answer the questions.
A. Between what times does the roller coaster dip below the platform?
B. What is the height and time at which Erin picture is taken during the roller coaster ride?
C. Erin picture is taken at the lowest point of the roller coaster.
35points!! To whoever help me with this.
Answer:
1) the factored form is y= ( x-5 ) ( x+4 )
2) the vertex is (4.5, -0.25)
3) the y intercept is when x equals 0 so it is at (0,20)
4) it opens upward and the vertex is (4.5, -0.25) the x intercepts are (4,0) and (5,0) and the y intercept is (0,20)
5)
a. it dips between 4 seconds and 5 seconds so the x intercepts are (4,0) and (5,0)
b. it is taken at the vertex aka the lowest point so the height is -0.25
Answer:
Part 1:
[tex]y= (x-4)(x-5)[/tex]
Part 2:
[tex](\frac{9}{2}, - \frac{1}{4})[/tex]
Part 3:
[tex]Y=20[/tex]
Part 5:
The height:
[tex]-\frac{1}{4}[/tex]
The time:
[tex]\frac{9}{2}[/tex]s
Step-by-step explanation:
[tex]y = x^{2} -9x+20[/tex] Is a quadratic equation.
Part 1:
We use [tex]x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex] to factor quadratic equations
[tex]y = x^{2} -9x+20[/tex]
a=1 b=-9 c=20
[tex]x = \frac {-(-9) \pm \sqrt {(-9)^2 - 4(1)(20)}}{2(1)}[/tex]
[tex]x = \frac {9 \pm \sqrt {81 -80}}{2}[/tex]
[tex]x = \frac {9 \pm {1}}{2}[/tex]
we solve both possibilities
[tex]x = \frac {9 + {1}}{2}=5[/tex]
[tex]x = 5[/tex]
[tex]x = \frac {9 -{1}}{2}=4[/tex]
[tex]x=4[/tex]
The factored form would be
[tex]y= (x-4)(x-5)[/tex]
Part 2:
We use the formula to find the x coordinate of the vertex of a parabola
[tex]V_{x}=\frac{-b}{2a}[/tex]
[tex]y = x^{2} -9x+20[/tex]
a=1 b=-9 c=20
[tex]V_{x}=\frac{9}{2}[/tex]
Now we substitute the value of x in [tex]y = x^{2} -9x+20[/tex] to find the value of the coordinate y of the vertex
[tex]y = \ (\frac{9}{2} )^{2} -9(\frac{9}{2}) +20\\ y= \frac{81}{4} -\frac{81}{2} +20\\ y= -\frac{1}{4}[/tex]
The vertex of the parabola is
Vertex:
[tex](\frac{9}{2}, - \frac{1}{4})[/tex]
Part 3:
the y-intercept is when the value of x = 0.
We substitute this value in [tex]y = x^{2} -9x+20[/tex]
[tex]y = 0^{2} -9(0)+20= 20[/tex]
The y-intercept is [tex]y=20[/tex]
Part 5:
A.
Between 4s and 5s
B and C.
Erin's photograph is taken at the lowest point of the roller coaster.
The lowest point of the parabola is the vertex.
The coordinate y of the vertex gives us the height and the coordinate x the time.
The height:
[tex]-\frac{1}{4}[/tex]
It is negative because it is below the point we take as zero.
The time:
[tex]\frac{9}{2}[/tex]s
Part 4:
The answer is the graph
A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find the value of the home after x years?
Answer:
Step-by-step explanation:
To build the equation we need to get the value.
120,000
Lets add the percent which is 1.055 since it is 5.5% added to nothing increasing
120,000(1.055)x
Answer:
120000(1.055)x
Step-by-step explanation
what other information do you need to prove triangle DAC=BCA by ASA
Answer:
∠ACD≅∠CAB
Step-by-step explanation:
According to SAS postulate if two sides and the included angle of ΔDAC are same to two sides and the included angle of ΔBCA. Then ΔDAC≅ΔBCA
But for the given figure
∠DAC≅∠BCA and
CA=AC (common in both triangle)
Hence we need ∠ACD≅∠CAB to prove that ΔDAC≅ΔBCA
find the solution of this system of equations
-6y=-50-4x
5x-6y=-49
Answer:
[tex](1,\ 9)[/tex]Step-by-step explanation:
Rewrite the first equation
[tex]-6y=-50-4x\\\\4x-6y=-50[/tex]
Now we have the following system of equations
[tex]4x-6y=-50\\5x-6y=-49[/tex]
To solve the system of equations multiply the first equation by -1 and add it to the second equation
[tex]-1*4x-(-1)*6y=-50*(-1)\\\\-4x+ 6y=50[/tex]
[tex]-4x+ 6y=50[/tex]
+
[tex]5x-6y=-49[/tex]
-----------------------------------
[tex]x + 0 =1\\\\x=1[/tex]
Now substitute the value of x in any of the two equations and solve for y
[tex]5(1)-6y=-49[/tex]
[tex]5-6y=-49[/tex]
[tex]-6y=-49-5[/tex]
[tex]-6y=-54[/tex]
[tex]y=\frac{54}{6}[/tex]
[tex]y=9[/tex]
The solution is:
[tex](1,\ 9)[/tex]
Ralph and Waldo start in towns that are 70 miles apart and travel in opposite directions for 4 hours.
Ralph travels
15 miles per hour faster than Waldo.
Let w stand for Waldo's speed and write algebraic expressions to answer the
following questions
a. How far did Waldo travel?
miles
b. What was Ralph's speed?
mph
C. How far did Ralph travel?
miles
d. What is the distance between Ralph and Waldo after the 4 hours?
miles
Answer:
Step-by-step explanation:
Let Waldo's speed = W
Let Ralph's speed = W + 15
A
Waldo's distance = speed * Time
Time = 4 hours.
Speed = w
distance = 4 * w
B
Ralph's speed is W + 15. It's not clear if you need a number. We'll get around to that later.
C
Ralph traveled 4*(W + 15)
D
4w + 70 + 4(W + 15) = d
You really can't get a definite answer to these questions. Even if you knew whether they were heading away from each other or towards each other it wouldn't help.
a construction crew is lengthening a road that originally measured 41 miles. The crew is adding one mile per day. The length, L(in miles), after d dayys of construction is given by following function L(d)=41+d what is the length of the road after 35 days
Answer:
L = 4d + 54
when d = 31 days
L = 4(31) + 54
L = 124 + 54
L = 178 miles
Step-by-step explanation:
The length of the road after 35 days of construction is 76 miles.
Explanation:The length of the road after 35 days can be calculated using the given function L(d) = 41 + d, where L represents the length in miles and d represents the number of days of construction. To find the length after 35 days, we substitute d = 35 into the function.
L(35) = 41 + 35
L(35) = 76
Therefore, the length of the road after 35 days of construction is 76 miles.
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Which values of P and Q result in an equation with exactly one solution? Px -43= -42x+Q. Choose all answers that apply. A. P= 42 and Q = 42. B. P= 43 and Q = -42. C. P= -43 and Q = -43. D.P = 42 and Q= 43
Answer:
All are valid
Step-by-step explanation:
Px - 43 = -42x + Q (rearrange)
x = (Q+43) / (P + 42) <----Substitute options for P & Q into this equation to see which combination gives exactly 1 solution for x
A) P=42, Q = 42; x = (42+43) / (42+42) = 1.011 (only 1 solution = valid)
B) P=43, Q = -42; x = (-42+43) / (43+42) = 0.012 (only 1 solution = valid)
C) P=-43, Q = -43; x = (-43+43) / (-43+42) = 0 (only 1 solution = valid)
D) P=42, Q = 43; x = (42+43) / (42+42) = 1.023 (only 1 solution = valid)
The function g(x) = 3x - 12x + 7 written in vertex form is g(x) = 3(x - 2)2 – 5. What is the vertex of g(x)?
A(-6, -5)
B (-2,-5)
C. (2,-5)
D (2,-5)
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ g(x)=3(x-\stackrel{h}{2})^2+(\stackrel{k}{-5})\qquad \qquad \stackrel{\textit{vertex}}{(2,-5)}[/tex]
Kinsley's age is 7 years less than twice Jacobs age if kensley is 13 years old how old is Jacob
Answer:
Age of Jacob is 10 years.
Step-by-step explanation:
Let the age of Jacob = x years and age of Kinsley = y years
Then by first statement " Kinsley's age is 7 years less than twice of Jacob's age"
y = 2x - 7
By second statement " Kensley is 13 years old "
y = 3 years
By putting y = 13 years in the equation
13 = 2x - 7
2x = 13 + 7
2x = 20
x = [tex]\frac{20}{2}[/tex] = 10 years
Therefore, age of Jacob is 10 years.
Answer:
The Answer is B. 10
Hope This Helps!
(06.02 mc) the equation of line cd is y=3x-3. Write an equation of a line perpendicular to line cd in slope intercept form that contains points 3,1
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 3 ← is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], hence
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (3, 1) into the partial equation
1 = - 1 + c ⇒ c = 1 + 1 = 2
y = - [tex]\frac{1}{3}[/tex] x + 2 ← equation of perpendicular line
Answer:
y = -1/3x + 2
got it correct on my test
what is the percent of change from 85 to 64? round to the nearest percent
Answer:
=25 %
Step-by-step explanation:
Percent decrease equals (original minus new) / original * 100 %
Percent decrease = (85-64)/ 85 * 100%
= 21/85 * 100%
=.247058824 * 100%
=24.7058824%
To the nearest percent
=25 %
what is the rise over run
Rise over run is another term for slope, with we can use to derive a linear equation.
The term rise over run in technical terms is the change of y over the change of x.
To find the rise over run, subtract the y terms and divide that by the x terms.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
You can use this to derive a linear equation as earlier mentioned by plugging in given points.
For example, a line passes through (3,4) with a rise over run of 3.
[tex]y=mx+b[/tex]
[tex]4=3(3)+b[/tex]
[tex]4=9+b[/tex]
[tex]b=-5[/tex]
So therefore the y intercept is -5, and the equation is [tex]y=3x-5[/tex]
HELP!!! THANK YOU SM
ACCURATE ANSWERS PLEASE
Answer: C
Step-by-step explanation:
1 + 2sin(x+pi)
1 is adding to the y, so it is a vertical shift of 1 unit,
2 is a stretch because it is multiplying to the sin,
and pi is adding to the x, so it is a phase shift.
need help little time left
bAnswer:
B)
Step-by-step explanation:
A line passes through the points (8,-1) and (-4,2). What is the y intercept of the line ?
Answer:
"Y intercept is1 "
Step-by-step explanation:
The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)
(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8
-x + 4 = 4y
y = (-1/4)x + 1 so that the y-intercept is 1
Answer:
"Y intercept is1 "
The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)
(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8
-x + 4 = 4y
y = (-1/4)x + 1 so that the y-intercept is 1
Step-by-step explanation:
Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive. What is the sum of the factors?
Answer:
13
Step-by-step explanation:
Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.
The difference of those two factors is -19. There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.
A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.
We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.
The question says the difference of the two factors is 19... can you spot in each list a pair of factors having a difference of 19? I see -3 and 16 and also 3 and -16.
The question also say the one of the greatest absolute value is positive... so that means it's a pair with +16, not -16.
The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.
The sum of -3 and 16 is 13.
Simplify (5√2-1)^2 please I need help
Answer:
51-10sqrt(2)
Step-by-step explanation:
(a-b)^2=a^2-2ab+b^2
(5sqrt(2)-1)^2=(5sqrt(2))^2-2(5sqrt(2))(1)+1^2
=5^2(2)-2(5sqrt(2))(1)+1^2
=25(2)-10sqrt(2)+1
=50-10sqrt(2)+1
=51-10sqrt(2)
Which is a true statement comparing the graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1?
The foci of both graphs are the same points.
The lengths of both transverse axes are the same.
The directrices of = 1 are horizontal while the directrices of = 1 are vertical.
The vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.
Answer:A
Step-by-step explanation:
Edge 21’
The true statement comparing the graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 is: The foci of both graphs are the same points.
True statement comparing the graphsWhen we look at graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 we would tend to see that the focus or foci of this two graph are the same point.
In order to know or determine that both graph are the same point or in order to determine each conic you have to focus on where the point crosses the axes.
Therefore the true statement comparing the graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 is: The foci of both graphs are the same points.
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A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
what is the value of a
Answer:
a = 2
Step-by-step explanation:
Let's find the equation of the line using the 2 points given.
Let's call -1 as x_1 and -5 as y_1
also, 4 as x_2 and 5 as y_2
The equation of line is :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let's plug the points and get the equation of the line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3[/tex]
Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:
[tex]y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2[/tex]
Answer: [tex]a=2[/tex]
Step-by-step explanation:
We know that this line passes through the point [tex](a,1)[/tex] where "a" is the unknown x-coordinate of that point and 1 is the y-coordinate.
We also know that this line passes through the points (-1, -5) and (4, 5).
Then, in order to find the value of "a", we can plot the known points and draw the line (Observe the image attached).
You can observe in the image attached that the point whose y-coordinate is 1 is the point (2,1). Therefore, the value of "a" is:
[tex]a=2[/tex]
Which undefined geometric term is described as a location on a coordinate plane that is designed by an ordered pair (x,y) ?
Answer:
Point
Step-by-step explanation:
Answer:
the answer is D
Step-by-step explanation:
I got it right on E2020
A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The company earned 68 billion dollars from 2008 to 2018.
The company earned 68 billion dollars in 2008.
The company earned 10 billion dollars from 2008 to 2018.
The company earned 10 billion dollars in 2008.
Answer:
The company earned 68 billion dollars in the year 2008..
Step-by-step explanation:
This is because the time t is the number of years since the END of 2008. The time t = 0 at the end of 2008, so the earnings = 0^2 + 10(0) + 68 = 68 billion.
Answer:
option B
Step-by-step explanation:
A particular company's net sales is modeled by the expression (t² + 10t + 68)
Where t represents number of years since the end of year 2008.
In this expression 68 is the constant term which represents the earning of the company before 2008. or in year 2008.
The company earned 68 billion dollars in 2008.
Therefore, option B is the answer.
Find a, b, and c.
A. a = 12,b = 6 root 3,c = 3 root 6
B. a = 12, B = 12 root 2, c = 3 root 6
C. a = 6 root 3, b = 12 root 3, C = 6 root 2
D. a = 6 root 3, b = 12 root 3,c= 6 root 2
Answer:
Option C.
[tex]a=6\sqrt{3}[/tex]
[tex]b=12[/tex]
[tex]c=6\sqrt{2}[/tex]
Step-by-step explanation:
step 1
Find the value of a
we know that
[tex]tan(60\°)=a/6[/tex]
Remember that
[tex]tan(60\°)=\sqrt{3}[/tex]
so
[tex]a/6=\sqrt{3}[/tex]
[tex]a=6\sqrt{3}[/tex]
step 2
Find the value of b
we know that
[tex]cos(60\°)=6/b[/tex]
Remember that
[tex]cos(60\°)=1/2[/tex]
so
[tex]6/b=1/2[/tex]
[tex]b=12[/tex]
step 3
Find the value of c
we know that
[tex]cos(45\°)=c/b[/tex]
[tex]cos(45\°)=c/12[/tex]
Remember that
[tex]cos(45\°)=\sqrt{2}/2[/tex]
[tex]c/12=\sqrt{2}/2[/tex]
[tex]c=6\sqrt{2}[/tex]
Answer:
C.
Step-by-step explanation:
Which equation shows an example of the associative property of addition?
(-7 + 1) + 71 = -7+ (i + 78)
(-7 + 1) + 7i = 71 +(-7i+1)
71% (-77 + 1) = (71-71) + (7ix)
(-71 + 1) + 0 = (-71 +1)
D
(-71+1) + 0 = (-71+1)
This is because the whole equation involves addition thus it is an example of associative property of addition
Answer:
(-71 + 1) + 0 = (-71 +1)
Step-by-step explanation:
Given 3 numbers: a,b,c
Associative property of addition: (a + b) + c = a + (b + c)
On this case: a= -71
b = 1
c = 0
(a + b) + c = (-71 + 1) + 0 = -70 + 0 = -70
(-71 + (1 + 0)) = (-71 + 1) = -70
Both the sums are equal to -70 and hence the associative property of addition for the three numbers a= -71, b = 1, c= 0 holds.
All the other options in the question contain a reference to variable i and does not have the same three values a,b,c on both sides of the equality. So they do not represent the associative property.
A driver runs over a nail, puncturing the tire without causing a leak. The position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table.
Time (s) Approximate height of the nail off the ground (inches)
0 0
0.01 2.1
0.02 7.6
0.03 14.9
0.04 21.5
0.05 25.5
0.06 25.5
0.07 21.5
Which key features of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?
A. period
B. minimum
C. maximum
D. amplitude
Answer: period
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
It is given that a driver runs over a nail, puncturing the tire without causing a leak.
Tire of a car represents a periodic function because after a particular time the tire comes its initial stage and that particular time interval is called a period.
It means period is the key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire.
Therefore the correct option is A.
Long division 639 divided by 8
Answer:
The answer is 79.875
Hope this helps!
Answer:
79.875
Step-by-step explanation:
79.875
8/639
-56
______
079
-072
_______
0070
-0064
_______
0060
-0056
________
0040
-0040
________
0000
which undefined term is used to define an angle ?
line-
plane-
Point-
ray-
???
Answer:
the right answer is point
Step-by-step explanation:
The Undefined term that is used to define an angle is; a point.
How to represent an angle?An angle is defined as the union of two rays with a common endpoint. The common end point is known as the vertex of the angle while the rays are known as the sides of the angle.
Now, angle can be named in different ways like use of capital letters, vertex of the angle, by placing any number or symbol at the vertex in the interior of the angle and other ways.
However, the undefined term that is used to define an angle is called "point".
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64,-48,36,-27 which formula can be used to describe the sequence
Answer:
see explanation
Step-by-step explanation:
These are the terms of a geometric sequence with n th term formula
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
r = [tex]\frac{-48}{64}[/tex] = [tex]\frac{36}{-48}[/tex] = - [tex]\frac{3}{4}[/tex]
the first term a = 64, hence
[tex]a_{n}[/tex] = 64 [tex](-3/4)^{n-1}[/tex]
The math club is experiencing a growth in membership. On average, they are seeing a growth of 3% each week. If they started with 10 members which function, S(x), represents the number of members in the science club after x weeks?
Answer:
[tex]s(x)=10(1.03)^{x}[/tex]
Step-by-step explanation:
Let
x -----> the number of weeks
S ----> the number of members in the science club
In this problem we have a exponential function of the form
[tex]s(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
we have
[tex]a=10\ membrers[/tex]
[tex]r=3\%[/tex]
[tex]b=100\%+3\% =103\%=103/100=1.03[/tex]
substitute
[tex]s(x)=10(1.03)^{x}[/tex]
Which table represents a linear function with a greater y-intercept than that of the function represented in the graph?
A.
x y
0, 3
6, -39
B.
x y
-2, 0
0 ,2
C.
x y
0, 5
5, -45
D.
x y
-2, 1
0, 4
E.
x y
0, -7
4 ,11
Answer:
C.Step-by-step explanation:
The y-intercept of the function represended in the graph is 4 → (0, 4).
The table C. represents a linear function with a greater y-intercept (0, 5) → 5.
What is the length of the hypotenuse in the right triangle shown below?
Picture needed. not enough info
Answer:
a² + b² = c², where a and b are the legs and c is the hypotenuse.