Answer:
[tex](1,\, 10)[/tex].
Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to [tex]x[/tex]. Make use of the power rule to find the following:
[tex]g^\prime(x) = 3\, x^2 - 2\, a\, x[/tex].
[tex]h^\prime(x) = 2\, (2\, x) + b = 4\, x + b[/tex].
The question states that the graphs of [tex]g(x)[/tex] and [tex]h(x)[/tex] touch at [tex]x = 1[/tex], such that [tex]g^\prime(1) = h^\prime(1)[/tex]. Therefore:
[tex]3 - 2\, a = 4 + b[/tex].
On the other hand, since the graph of [tex]g(x)[/tex] and [tex]h(x)[/tex] coincide at [tex]x = 1[/tex], [tex]g(1) = h(1)[/tex] (otherwise, the two graphs would not even touch at that point.) Therefore:
[tex]1 - a + 6 = 2 + b + 3[/tex].
Solve this system of two equations for [tex]a[/tex] and [tex]b[/tex]:
[tex]\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}[/tex].
Therefore, [tex]a = -3[/tex] whereas [tex]b = 5[/tex].
Substitute these two values back into the expression for [tex]g(x)[/tex] and [tex]h(x)[/tex]:
[tex]g(x) = x^3 + 3\, x^2 + 6[/tex].
[tex]h(x) = 2\, x^2 + 5\, x + 3[/tex].
Evaluate either expression at [tex]x = 1[/tex] to find the [tex]y[/tex]-coordinate of the intersection. For example, [tex]g(1) = 1 + 3 + 6 = 10[/tex]. Similarly, [tex]h(1) = 2 + 5 + 3 = 10[/tex].
Therefore, the intersection of these two graphs would be at [tex](1,\, 10)[/tex].
Please don't troll!!!!!!!
Answer:
Ben = $ 41
Kaden = $ 31
Step-by-step explanation:
Let initially Ben has $ p and then Kaden has $ (p - 10).
After that
Ben has= $ (p + 4)
Kaden has = $ (p- 10 + 4) = $ ( p - 6)
According to the question,
[tex]p- 6 = \frac{7}{9}\times (p+4)\\\\9 p- 54 = 7 p + 28 \\\\2 p = 82\\\\p =41[/tex]
Initially Ben has $ 41 and Kaden has $ 31.
Can someone please answer this I’ll give brainliest
Answer:
Step-by-step explanation:
If you look at the diagram, you notice there are two triangular bases and three rectangular faces.
Therefore, the surface area, or the total area of all the bases and faces, would be the area of one triangular base multiplied by 2 and the area of each rectangular face
area of triangle = (1/2)*height*base
area of triangular base = (1/2)*15*28 = 210 cm^2
area of rectangle = base*height
area of rectangular face #1 = 25*30 = 750 cm^2
area of rectangular face #2 = 17*30 = 510 cm^2
area of rectangular face #3 = 28*30 = 840 cm^2
total surface area = 2*210 + 750 + 510 + 840 = 2520 cm^2
Simplify the expression....
Answer:
−3x^2+2x /x−2
Step-by-step explanation:
4x−9x^3/ 3x^2−4x−4
= −9x^3+4x /3x^2−4x−4
= x(−3x+2)(3x+2) /(3x+2)(x−2)
= −3x^2+2x /x−2
A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.
Answer:
Our two numbers are:
[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]
Or, approximately 7.66 and 3.66.
Step-by-step explanation:
Let the two numbers be a and b.
One positive real number is four less than another. So, we can write that:
[tex]b=a-4[/tex]
The sum of the squares of the two numbers is 72. Therefore:
[tex]a^2+b^2=72[/tex]
Substitute:
[tex]a^2+(a-4)^2=72[/tex]
Solve for a. Expand:
[tex]a^2+(a^2-8a+16)=72[/tex]
Simplify:
[tex]2a^2-8a+16=72[/tex]
Divide both sides by two:
[tex]a^2-4a+8=36[/tex]
Subtract 36 from both sides:
[tex]a^2-4a-28=0[/tex]
The equation isn't factorable. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -28. Substitute:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]
So, our two solutions are:
[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]
Since the two numbers are positive, we can ignore the second solution.
So, our first number is:
[tex]a=2+4\sqrt{2}[/tex]
And since the second number is four less, our second number is:
[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]
Answer:
[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]
Step-by-step explanation:
Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:
[tex]x^2+(x-4)^2=72[/tex]
Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]x^2+x^2-2(4)(x)+16=72[/tex]
Combine like terms:
[tex]2x^2-8x+16=72[/tex]
Subtract 72 from both sides:
[tex]2x^2-8x-56=0[/tex]
Use the quadratic formula to find solutions for [tex]x[/tex]:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]
In [tex]2x^2-8x-56[/tex], assign:
[tex]a\implies 2[/tex] [tex]b \implies -8[/tex] [tex]c\implies -56[/tex]Solving, we get:
[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]
Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].
Verify:
[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]
A(1,7) B(6,4) and C(5,5) are three points in a plane
1. Find the equations of the perpendicular bisectors of AB and AC
Determine the point of intersection of the perpendicular bisectors in (I)
Answer:
Step-by-step explanation:
Middle point of AB
x(m) = (6+1)/2 = 7/2
y(m) = (7+4)/2 = 11/2
slope of the line that contains AB
(4-7)/(6-1) = -3/5
eqaution of the perpendicular bisector
y-11/2 = 5/3(x-7/2)
y = 5/3x -35/6 + 11/2
y = 5/3x + (-35 + 33)/6
y = 5/3x -1/3
Middle point of AC
x(m) = (1+5)/2 = 3
y(m) = (7+5)/2 = 6
Slope of the line that contains AC
(5-7)/(5-1) = -1/2
equation of the perpendicular bisector
y-6 = 2(x-3)
y = 2x -6 + 6
y = 2x
Point of intersection
y= 5/3x -1/3
y = 2x
2x = 5/3x - 1/3
6x = 5x - 1
x = -1
y = -2
P(-1,-2)
Answer:
(1,7)
Step-by-step explanation:
Given:
A(1,7)
B(6,4)
C(5,5)
Solution:
Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)
Slope of AB = (4-7)/(6-1) = -3/5
Perpendicular bisector of AB:
L1: y - 11/2 = -(3/5)(x-7/2) ............(1)
Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)
Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2
perpendicular bisector of AC:
L2: y-6 = -(1/2)(x-3) ..........."(2)
To find the point of intersection,
(1)-(2)
-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2
1/2 = -x/10 + 6/10
x/10 = 1/10
x = 1
substitute x in (1)
y = 3/2+11/2 =7
Therefore Point of intersection is (1,7)
The HCF and LCM of two numbers is 9 and 459 respectively if one the number is 27 the other number is (1)
Answer:
153
Step-by-step explanation:
[tex]other \: number = \frac{9 \times 459}{27} \\ \\ = \frac{459}{3} \\ \\ = 153[/tex]
Answer:
Other number is 153
Step-by-step explanation:
Usually, the product of the HCF and LCM will be the product of the 2 numbers in question.
The HCF and LCM are given as 9 and 459.
While one of the numbers used to find the HCF & LCM was 27.
Let the other number be y.
Thus;
27y = 459 × 9
y = 459 × 9/27
y = 153
Find f ′(x) for f(x) = cos (5x2).
Answer:
I think its No Solution
Step-by-step explanation:
Hope it helps
A) x = -2
B) y =2
C) y= -2
Answer:
Step-by-step explanation:
This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.
The form that the parabola is currently in is
[tex]y=a(x-h)^2+k[/tex] so that means that [tex]a=\frac{1}{8}[/tex]. We can use that to solve for p in the formula
[tex]p=\frac{1}{4a}[/tex] so
[tex]p=\frac{1}{4(\frac{1}{8}) }[/tex] which simplifies to
[tex]p=\frac{1}{\frac{1}{2} }[/tex] which gives us that
p = 2. Now to find the directrix:
y = k - p becomes
y = 0 - 2 so
y = -2, choice A.
joey is going shopping for a new pair of sneakers. He finds a pair that have an original price of $155. They are on sale today for 30% off. How much does Joey pay for the sneakers including 8% sales tax?
Answer:, Joey will pay $117.18 for sneakers.
Step-by-step explanation:
Given: original price = $155
Discount rate = 30%
Tax rate = 8%
Price after discount = Original price - (Discount) x (original price)
[tex]= 155-0.30\times 155\\\\=155-46.5\\\\=\$\ 108.5[/tex]
Tax = Tax rate x (Price after discount)
[tex]= 0.08 \times 108.5[/tex]
= $ 8.68
Final price for sneakers = Price after discount + Tax
= $ (108.5+8.68)
= $ 117.18
Hence
Which are the solutions of the quadratic equation?
x² = 7x + 4
Answer:
[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
What type of angel is 107 degrees
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Answer:
An obtuse angle
Step-by-step explanation:
Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,
acute: degree measure between (0) and (90) degrees
right: exactly (90) degrees,
obtuse: degree measure between (90) and (180) degrees
reflex: degree measure between (180) and (360) degrees
What is the domain of the function y=%/x-1?
O-
o -1 < x < oo
0
O 1
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x - 1}[/tex]
Required
The domain
The given function is cubic root; there are no restrictions on cubic root functions
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
A battery with a voltage of 3 V provides a voltage of 0.56 C to some circuits. Calculate the electrical power provided by this battery
Answer:
The power is 1.68 W.
Step-by-step explanation:
Voltage, V = 3 V
charge, q = 0.56 C
time, t = 1 s
The power is given by
P = V q/t
P = 3 x 0.56 / 1
P = 1.68 W
So I'm just making sure...
Complementary angles add up to 90°
Supplementary angles add up to 180°
I've seen many different answers so I am just double checking. Thanks.
Answer:
This is correct.
Step-by-step explanation:
Answer:
Yes...You are right... hope it helps
A chair rental company charges $100 for delivery plus $3 per
chair. You want to order 200 chairs for a concert. How much
will it cost?
O a. $300
O b. $600
O c. $700
O d. None of the above
above
Answer: 700
Step-by-step explanation: 3 x 200 + 100
Answer:
c.$700
Step-by-step explanation:
3x+100 3 per chair=3x plus the additional 100 dollar fee
3(200)+100
600+100
700
Please help. Thank you
Given:
[tex]PQRS\sim TUVW[/tex]
In the given figure, PS=x, RS=35, UV=20, VW=25 and TW=15
To find:
The scale factor from PQRS to TUVW.
Solution:
We have,
[tex]PQRS\sim TUVW[/tex]
We know that the corresponding sides of similar figures are proportional. The scale factor is the ratio of one side of image and corresponding side of preimage.
The scale factor is:
[tex]k=\dfrac{VW}{RS}[/tex]
[tex]k=\dfrac{25}{35}[/tex]
[tex]k=\dfrac{5}{7}[/tex]
Therefore, the scale factor from PQRS to TUVW is [tex]k=\dfrac{5}{7}[/tex].
Line p is parallel to line q
Which set of statements about the angles is true ?
Need answer to this maths question plssss
Answer:
The fourth angles is 105
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360
3*85 = 225
Let the fourth angle be x
225 +x = 360
x = 360 -225
x =105
PLSSS, NEED ANSWER. Find the midpoint of the line segment with end coordinates of (-2,-5 and 3,-2
). Give coordinates as decimals where apropriate
Answer:
1, -3.5
Step-by-step explanation:
Answer:(0.5,-3.5)
Step-by-step explanation:
(-2+3/2)/2, (-5-2)/2
0.5,-3.5
Help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4/8 = 1/2
Step-by-step explanation:
hope it thepled u
Hurry !!Answer each question about the following
geometric series
10
k-1
What is the first term of the series?
a =
S10 - 3(2)k-1
RETRY
k-1
How many terms are in the series?
1
2
9
✓
10
COMPLETE
Answer:
last term is 1536
Value of the geometric series is 3,069
Step-by-step explanation:
took one for the team
There are 10 terms in the geometric series.
And, The first term of the series is, 3
We know that;
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The geometric series is,
⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹
Where, n is from 1 to 10.
Thus, We get;
There are 10 terms in the geometric series.
And, For first term;
Put n = 1;
⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹
⇒ S₁₀ = ∑ 3 (2)¹⁻¹
⇒ S₁₀ = ∑ 3 (2)⁰
⇒ S₁₀ = ∑ 3 × 1
⇒ S₁₀ = 3
Thus, The first term of the series is, 3
Learn more about the geometric sequence visit:
https://brainly.com/question/25461416
#SPJ7
Six teammates are competing for first, second, and third place in a race.
How many possibilities are there for the top three positions?
20
30
120
240
Step-by-step explanation:
there Are 120 possibilities for the top three positions
We will see that there are 120 different possibilities for the top 3 positions.
How many possibilities are there for the top three positions?Here we need to count the number of options for each of the positions.
For the first position, there are 6 options (6 team members).For the second position, there are 5 options (because one is already in the first position).For the third position, there are 4 options.The total number of different combinations is given by the product between the numbers of options, we will get:
C = 6*5*4 = 120
There are 120 different possibilities for the 3 positions.
If you want to learn more about combinations, you can read:
https://brainly.com/question/11732255
#SPJ2
Help please I keep missing the middle one
Answer:
4 + (1/3)w + w = 24
subtract 4 from both sides
(1/3)w + w = 20
multiply both sides by 3 to clear the fraction
w + 3w = 60
4w = 60
Divide both sides by 4
w = 15
Expand 3(c + 3).
3(c + 3) =
Answer:
3c + 9
Step-by-step explanation:
Remember to multiply everything in the brackets by the number outside the brackets.
Find the volume of the irregular
figure
1 cm
3 cm
?] cm3
3 cm
1 cm
10 cm
5 cm
Answer:
Step-by-step explanation:
volume of reqd. figure=10×5×1+3×3×1=50+9=59 cm³
If x is 6, then 7x =
Answer:
42
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
x = 6
7x
Step 2: Evaluate
Substitute in variables: 7(6)Multiply: 4215
9
determine the value
coso
Answer:
36.87°
Step-by-step explanation:
Given the right angle triangle :
To obtain the value of Cosθ ; we use the trigonometric relation :
Cosθ = Adjacent / Hypotenus
The adjacent angle isn't given :
Opposite = 9 ; hypotenus = 15
Adjacent = √(hypotenus ² + opposite ²)
Adjacent = √(15² - 9²)
Adjacent = √(225 -81)
Adjacent = √144 = 12
Hence,
Cos θ = 12/15
θ = Cos^-1(12/15)
θ = 36.87°
Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges. Write a formula that will help her determine how much she will make in a week. Let's Let a= total amount earned, h= hours worked in one week, n= number of bouquets she arranged, and b= bonus amount for bouquets
Answer: a = 7.5h + bn
Step-by-step explanation:
Since Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.
where,
a = total amount earned,
h= hours worked in one week,
n = number of bouquets she arranged
b= bonus amount for bouquets
Then, the formula that will help her determine how much she will make in a week will be:
a = (7.5 × h) + (b × n)
a = 7.5h + bn
The formula is a = 7.5h + bn.
What is the x value of the solution to the system of equations
4y=2x+8
Y=-x+2
Answer:
x=0;y=2
Step-by-step explanation:
4(-x+2)=2x+8 -4x+8=2x+8 -4x-2x=8-8 -6x=0 x=0 y=-x+2 y=0+2 y=2
Please Help. Thank you
Answer:
7/5 is the scale factor
Step-by-step explanation:
