Answer:
This implies that
x2+2ax=4x−4a−13
or
x2+2ax−4x+4a+13=0
or
x2+(2a−4)x+(4a+13)=0
Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.
Hence we get that
(2a−4)2=4⋅1⋅(4a+13)
or
4a2−16a+16=16a+52
or
4a2−32a−36=0
or
a2−8a−9=0
or
(a−9)(a+1)=0
So the values of a are −1 and 9.
Step-by-step explanation:
Answer:
[tex]\frac{492}{65}[/tex]
Step-by-step explanation:
Using the trigonometric identity
sin²A + cos²A = 1 , then
sinA = [tex]\sqrt{1-cos^2A}[/tex] thus
sinA = [tex]\sqrt{1-(5/13)^2}[/tex]
= [tex]\sqrt{1-\frac{25}{169} }[/tex]
= [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex] , then
tanA = [tex]\frac{sinA}{cosA}[/tex] = [tex]\frac{\frac{12}{13} }{\frac{5}{13} }[/tex] = [tex]\frac{12}{5}[/tex]
Thus
2tanA + 3sinA
= 2 × [tex]\frac{12}{5}[/tex] + ( 3 × [tex]\frac{12}{13}[/tex] )
= [tex]\frac{24}{5}[/tex] + [tex]\frac{36}{13}[/tex]
= [tex]\frac{312}{65}[/tex] + [tex]\frac{180}{65}[/tex]
= [tex]\frac{492}{65}[/tex]
Transform the quadratic function defined by y=ax2+bx+c into the form y=a(x-h)2+k 1.Y=x2-6x-3 2.Y=5x2-20x-5
Answer:
1) y = (x-3)²-12
2) y = 5(x-2)²-9
Step-by-step explanation:
Given the quadratic expressions
y=x²-6x-3
We are to transform it in the form y=ax²+bx+c
y=(x²-6x)-3
Complete the square of the expression in parenthesis
y = (x²-6x + (6/2)² - (6/2)²)-3
y = (x²-6x+3²-3²)-3
y = (x²-6x+9-9)-3
y = (x²-6x+9)-12
y = (x²-3x-3x+9)-12
y = x(x-3)-3(x-3)-12
y = (x-3)(x-3)-12
y = (x-3)²-12
Hence the transformation is y = (x-3)²-12 where a = 1 and k = -12
For the quadratic equation
y=(5x²-20x)-5
y = 5(x²-4x)- 5
Complete the square of the expression in parenthesis
y = 5(x²-4x+4-4)- 5
y = 5(x²-4x+4)-9
y = 5(x-2)²-9
Hence the transformation is y = 5(x-2)²-9 where a = 5 and k = -9
if tan=5/12 what is sin
Answer:
5/13
Step-by-step explanation:
by using SO TO CA
H A H
sin can be obtained
a. Is this an arithmetic sequence? How do you know?
b. How much does the investment grow each year?
c. How much money did the investment start out as?
d. What sequence equation would represent this graph?
e. What would the value of the investment be after another 10 years?
f. What would the value of the investment be after a total of 20 years?
Answer:
a. Yes. The difference is common and equal to $1750
b. $1750
c. $20000 was initial investment
d. This is linear equation with start point of 20000 and slope of 1750:
y = 1750x + 20000e. After another 10 years (on the top of 5 given) the investment will be:
y = 1750*15 + 20000 = $46250f. After 20 years the value of investment will be:
y = 1750*20 + 20000 = $55000A radio station charges an initial fee for broadcasting advertisements plus a rate based on the length of the advertisement in seconds. The table below shows the total charges for advertisements of different lengths.
Which equation BEST represents the linear relationship between n, the length in seconds of an advertisement and c, the total charge of the advertisement?
a. c=3n+180
b. c=4n+120
c. c=2n+210
d. c=5n+150
p.s graph is attached
Answer:
It's a.
Step-by-step explanation:
15s*3+180＝225
30s*3+180＝270
60s*3+180＝360
30s*3+180＝270
the total cost of ticket for a play is $95. tickets cost 2.50 one child and $5.00 for an adult. write equations that will represent the number of children and adult,describe the variable each representation ?
Answer:
2.50C +5.00A=95
Step-by-step explanation:
In this equation, C represents the number of children attending and the A represents the amount of adults attending.
Choose a value for b so that the relation below is not a function.
Answer:
B. -2
Step-by-step explanation:
A relation that is not a function would have one x-value having two different corresponding y-values.
If we choose -2 to represent b I the relation, the relation would not be a function. This is because, we there would be two different y-values, 8 and 1, that are assigned to one x-value, which is -2 ==> (-2, 8) and (-2, 1).
Chad and Eric left a 20% tip after having lunch at a restaurant. Chad's lunch cost $10.
Which equation can you use to find x, the cost of Eric's lunch?
Group of answer choices
A) 0.2(x + 10) = 5
B) 0.2x = 10 + 5
C) 0.2x + 5 = 10
D) 0.2x + 10 = 5
Answer:
The equation used to find x, the cost of Eric's lunch is [tex]\mathbf{0.2(x+10)=5}[/tex]
Option A is correct option.
Step-by-step explanation:
Chad and Eric left a 20% tip after having lunch at a restaurant.
Cost of Chad Lunch = $10
Let Cost of Eric's lunch = x
So, Total cost of Chad and Eric's Lunch = x+10
Now, they left a 20% tip
it means 20% of total cost of lunch
20% can be written as 0.2
So, 0.2 of total cost of lunch is tip of the meal
We can write: 0.2 of (x+10)
or 0.2(x+10)
Looking at options, considering $5 was the amount of tip, the final equation will be:
[tex]0.2(x+10)=5[/tex]
So, the equation used to find x, the cost of Eric's lunch is [tex]\mathbf{0.2(x+10)=5}[/tex]
Option A is correct option.
As an estimation we are told 5 miles is 8 km.
Convert 27.4 miles to km.
Answer:
≈ 44 kmStep-by-step explanation:
5 miles = 8 km
Then:
1 mile = 8/5 kmThen 27.4 miles is:
27.4*8/5 = 43.84 ≈ 44 kmToby picks a 4-digit number.
It is larger than 7999 and it is a multiple of 5.
How many different numbers could he have picked?
Answer:
Total different numbers = 400
Step-by-step explanation:
Assume;
Smallest number bigger than 7999( multiple of 5) = 8,000
largest 4 digit number multiple of 5) = 9,995
Computation:
a = 8,000
d = 5
an = 9,995
an = a + (n-1)d
9,995 = 8,000 + (n-1)5
1,995 = (n-1)5
399 = n-1
n = 400
Total different numbers = 400
If the diameter of the following circle is tripled, which of the following expressions could be used to find the area of the
new circle?
18 in
3254.34 in 2
31113.04 in
9(1017.36 in
9.254.34 in
Answer:
my answer is a bit different but kinda similar ig.
254.34in^2
Step-by-step explanation:
Radius = Diameter/2 18/2 = 9
Area of circle= pi(3.14) x r^2
A= (3.14) x 9^2
A= (3.14) x 81
A= 254.34in^2
Answer:
I can confirm that the answer is 3(254.34 in.2). I did it on Odyssey
Step-by-step explanation:
What is the y-intercept of the line 2x - 3y = -6?
Answer:
2
Step-by-step explanation:
substitute x=0 and find y
plz help me Quick l need helpppp
You burn 7 calories per minutes swimming. Your friend burns 273 calories running and then 11 calories per minutes swimming. You each swim for the same number of minutes. Find the difference in the amounts of calories burned by you and your friend
Answer:
168
Step-by-step explanation:
What is the value of x?
PLEASE I NEED HELP WITH THISSS ASAP!!!! I WILL GIVE BRAINLIEST!
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Given:
The function is
[tex]f(x)=\log_5(x)[/tex]
To find:
The graph of the given function.
Solution:
We have,
[tex]f(x)=\log_5(x)[/tex]
At x=1,
[tex]f(1)=\log_5(1)[/tex]
[tex]f(1)=0[/tex] [tex][\because \log_a(1)=0, a>0][/tex]At x=5,
[tex]f(5)=\log_5(5)[/tex]
[tex]f(5)=1[/tex] [tex][\because \log_aa=1][/tex]
So, the graph of given function passes through the points (1,0) and (5,1). Only graph in option A passes through these two points.
Therefore, the correct option is A.
you are purchasing a subscription to spotify premium.the subscription costs 15$ per month what's the dependent variable and independent variable
Answer:
$15 dependant variable, month is the independent variable
Bus A leaves the station every 30 mins bus b leaves the station every 20 mins at 10 am both buses leave the station together work out the next time both buses leave at the same time
Answer: 11am
Step-by-step explanation:
To solve this, we have to calculate the lowest common multiple of 20 and 30. This will be:
20 = 20, 40, 60, 80, 100
30 = 30, 60, 90, 120, 150.
Here, the lowest common multiple is 60.
Therefore, we add 60 minutes to 10am. This will be:
= 10am + 1 hour
= 11 am
The next time that both buses leave at the same time would be 11am
For the function shown below, find f(2): f(x)=2x^4-8x^2+5x-7
Answer:
F(2)=3
Step-by-step explanation:
Ms.chin asked her students to use the properties of multiplication to rewrite the expression
Find the value of x that solves the system shown below.
y = 5x
2x - y = 18
Answer:
hope my answer is helpful to you
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A library had 570 books when it first opened. A year later, the number of books increased by 30%. How many books were there in the library a year later?
Answer: There were 741 books in the library a year later.
Step-by-step explanation:
Given: Total books in library = 570
Number of books increased by 30%.
One year later, Number of books in the library = (Total books in library) + 30% x (Total books in library)
= 570 + (0.30) x (570)
= 570 (1+0.30)
= 570 (1.30)
= 741
Hence, there were 741 books in the library a year later.
the radius of a bubble increases by 4%. Calculate the percentage increase in its (a) surface area (b) volume (to three significant figures )
Answer:
Step-by-step explanation:
Given that the radius of a bubble increases by 4%.
Let r be the radius of the spherical bubble, so the new radius of the sphere
[tex]R= r+0.04r = 1.04r\cdots(i)[/tex]
(a) Surface area of the bobble,
[tex]s=4\pi r^2[/tex]
So, the rate of increase of surface area = [tex]4\pi R^2 -4\pi r^2= 4\pi(R^2-r^2)[/tex]
The percentage change in the surface area [tex]= \frac {4\pi(R^2-r^2)}{4\pi r^2}\times 100[/tex]
By using equation (i)
The percentage change in the surface area = [tex]\frac {(1.04r)^2-r^2}{ r^2}\times 100[/tex]
[tex]=(1.04^2-1)\times 100[/tex]
=8.160%
Therefore, the percentage change in the surface area is 8.160%
(b) The volume of the sphere = [tex]4/3 \pi r^3[/tex]
So, the change in the volume = [tex]4/3 \pi R^3-4/3 \pi r^3[/tex]
Percentage change in the volume =
[tex]\frac {4/3 \pi R^3-4/3 \pi r^3}{4/3 \pi r^3}\times 100[/tex]
[tex]=(1.04^3-1)100[/tex] [by using equation (i)]
=12.486%
Therefore, the percentage change in the volume is 12.486%.
You have several options to add to your brand new car: leather seats, heated seats, sunroof, tinted windows, and back up camera. How many different ways can the car be built?
Answer:
The number of different ways the car can be built is 31 different ways
Step-by-step explanation:
The given options are'
1), Leather seats, 2) Heated seats, 3) Sunroof, 4) Tinted windows, 5), back up camera
Therefore, the number of different ways the car can be built, n, is given as follows;
n = ₅C₁ + ₅C₂ + ₅C₃ + ₅C₄ + ₅C₅
n = 5 + 10 + 10 + 5 + 1 = 31 different ways
The number of different ways the car can be built = n = 31 different ways
Find x. x2 = 576.
pls pls pls help
Answer:
x=24 or x= −24
Step-by-step explanation:
Step 1: Take square root.
x = ± √576
x=24 or x= −24
Yo can I get some help ?
the sum of the interior angles of a polygon is 1980°.how many sides has the polygon
Answer:
sum of interior angle of polygon = (2N-4) X 90 where N =number of sides
so (2N-4)x90=1980
therefore N=13.
therefore polygon has 13 sides
Answer:
To know how many sides has this polygon, knowing the sum of their interior angles, we can use this expression:
b = (n-2) * 180
Where b is the sum of the interior numbers and n the number of sides.
Knowing this, we can replace, as we kno w it
b = (n-2)) * 180
1980 = (n-2)*180
We can know solve the equation
We can use this distributive property to operate the parenthesis, which says that if we find this expression a(b+c), we can operate doing ab+ac, and, if we substract, we can also use it, as a(b-c) = ab-ac
1980 = (n-2)*180
1980 = 180n - 180*2 = 180n - 360
1980 = 180n - 360
1980 + 360 = 180n
[tex]\frac{1980+360}{180} = n.[/tex]
13 = n
So we know the polygon will have 13 sides..
I need help fast thanks
I have a hard time understanding this question
Answer:
22m+42 is the answer
Step-by-step explanation:
All you have to do is simplify and add the common factors.
Halle has $48 saved for a new computer. Then she receives birthday money giving her a total of $290 saved. How much birthday money did she receive?