Answer:
all negative number to -15
Determine the value of K that will cause f(x)=Kx^2+4x-3 to intersect the line g(x)=2x-7 at one point. SHOW ALL YOUR STEPS, DON'T USE DECIMALS INSTEAD USE FRACTIONS PLEASE!!!!!
Given:
The function are:
[tex]f(x)=Kx^2+4x-3[/tex]
[tex]g(x)=2x-7[/tex]
The graph of f(x) intersect the line g(x) at one point.
To find:
The value of K.
Solution:
The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.
We have,
[tex]f(x)=Kx^2+4x-3[/tex]
Differentiate this function with respect to x.
[tex]f'(x)=K(2x)+4(1)-(0)[/tex]
[tex]f'(x)=2Kx+4[/tex]
Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:
[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]
On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get
[tex]m=2[/tex]
So, the slope of the tangent line is 2.
[tex]2Kx_0+4=2[/tex]
[tex]2Kx_0=2-4[/tex]
[tex]x_0=\dfrac{-2}{2K}[/tex]
[tex]x_0=-\dfrac{1}{K}[/tex]
Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get
[tex]y_0=2x_0-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get
[tex]y_0=2(-\dfrac{1}{K})-7[/tex]
[tex]y_0=-\dfrac{2}{K}-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).
[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]
Multiply both sides by K.
[tex]-2-7K=-3-3K[/tex]
[tex]-2+3=7K-3k[/tex]
[tex]1=4k[/tex]
[tex]\dfrac{1}{4}=K[/tex]
Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].
Ms. Jones wants to paint her kitchen's wall. She knows that 2 gallons of paint cover 80 square feet, and each gallon costs $20.80. If the area of the kitchen is 320 square feet, how much will she pay to buy the gallons of paint needed? Round your answer to the nearest cent (HUNDRED TH), and write ONLY a number (NO $)
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer. PLEASE HELP ITS RLLY IMPORTANT
Find the slope of the line for each pair of points (-17, -5) (15, -13)
What is the measure of
60° because it's an equilateral triangle
Alyssa invested $180 in an account paying an interest rate of 8 and 3/8 % compounded annually. Lily invested $180 in an account paying an interest rate of 8 and 1/8 % compounded continuously. To the nearest hundredth of a year, how much longer would it take for Alyssa's money to triple than for Lily's money to triple?
Answer:
Step-by-step explanation:
Please check out the attachments for the solution :)
The diameter of a cylinder is twice the height (h) of the cylinder. Show that the total surface area of the cylinder is:
[tex]4\pi \ {h}^{2} [/tex]
Answer:
Please check explanations
Step-by-step explanation:
The diameter is twice the height;
if diameter is d and height is h
Then;
d = 2h
But, we know that the radius is half the diameter size. Which means that the diameter is twice the radius
Thus;
2r = 2h
Then r = h
Mathematically the total surface area of a cylinder is;
2pi r (r + h)
substitute h for r
2pi h(h + h)
= 2pi * h * 2h
= 4 pi h^2 (QED)
Which two intergers is
[tex] - \sqrt{} 116[/tex]
between
options: -13 and -12 or - 11 and - 10 or and - 10 and -9 or -14 and -13.
Answer:
Between-10 and -9
Step-by-step explanation:
Square root of 116 is 10.77. Since there’s a minuscule sign it’s -10.77
So it’s between -10 and -9
Evaluate the expression for x = 10 . 3x + 4(x - 8) - 14
Answer:
[tex]{ \tt{3x + 4(x - 8) - 14}} \\ = { \tt{3x + 4x - 32 - 14}} \\ = { \tt{7x + 46}}[/tex]
Which graph represents an exponential function?
Answer: where's the pic?
Step-by-step explanation:
Find the greatest common factor of 15 x²y³ and -18 x³yz.
_x--y--
Answer:
3x^2y
Step-by-step explanation:
Its common factor it this ^ this symbol represent power
What is the greatest common factor of the polynomial below?
12x2-9x
A. 3x2
B. 3x
C. 4x2
D. 4x
Answer:
3x
Step-by-step explanation:
factoring it we get
3x(4x-3)
Help me pleaseeeee!!!!!!!!
Answer:
140
Step-by-step explanation:
Angles 1, 2 and 3 are in a straight line,
Straight line has 180 degrees,
∠1 = ∠3 = 20
∠1 + ∠2 + ∠3 = 180
20 + ∠2 + 20 = 180
∠2 + 40 = 180
∠2 = 180 - 40
∠2 = 140
Kevin jogged 2 1/2 miles in 1/3 of an hour. What was his average rate in speed in miles per hour? Show your work.
Answer:
7.5 miles per hour
Step-by-step explanation:
Average Speed = Total Distance/Total Time
[tex]\frac{2 \frac{1}{2} }{\frac{1}{3} }[/tex]= 7.5 miles/hour
Answer from Gauthmath
What is the quotient ? 7-6 72 1 o 1 o 1 72 O 73 0 78
Answer:
A. 1/7^8
Step-by-step explanation:
Given
(7^-6) / 7²
Both numerator and denominator has the same base, so just one of the bases will be picked
Division sign changes to minus in indices
(7^-6) / 7²
= 7 ^(-6-2)
= 7^-8
= 1/7^8
Note: a^-b
= 1/a^b
The same rule is used at the last step of the calculation
Answer is
A. 1/7^8
y is directly proportional to the cube of x. If x is tripled, what happens to the value of y?
Answer:
it becomes 27 times larger
Step-by-step explanation:
y = k [tex]x^{3}[/tex]
vs.
y = k[tex](3x)^{3}[/tex]
y = k 27 x^3
A hall has 22 rows of chairs there are 18 chairs in each row how many extra rows of chairs are needed to seat 468
Answer:
Total chairs = 18×22= 396
so no. of extra chairs need = 468-396 = 72
Now( 72/18) rows = 4 rows
Therefore 4 more rows are needed here
Hope it helps you
Answer: 4
Step-by-step explanation:
The amount of chairs in the hall can be found by multiplying 22 by 18 and getting 396. The amount of chairs needed is 468, so 468-396 gets you the amount of chairs still needed and the number 72. There are 18 chairs in each row, and 72/18 is 4. So 4 more rows are needed.
im giving brainliest pls heelp
Maria bought a stock for x dollars, and she sold it at a profit of 20 %. Write a mathematical expression for the selling price.
120x
1.2 x
0.12x
12x
Answer:
No entendí lo siento
Step-by-step explanation:
Jummm
B)1.2 x is a mathematical expression for the selling price.
What is the selling price?The selling price is the charge that a purchaser will pay to purchase a product or a commodity. It's miles a price above the value price and consists of a percentage of income additionally. Cost price is the price at which the seller purchases the product or the commodity.
Maria bought a stock for x dollars.
Cost of stocks = x dollars.
sold it at a profit of 20 %.
The selling price is given below.
= x + 20%
= 1.2x
Learn more about the selling price here: https://brainly.com/question/1153322
#SPJ2
In the picture below, which lines are lines of symmetry for the figure?
A. only 1
B. 1, 2, and 3
C. 1 and 3
D. only 3
(40/5)-7+2? I know the answer but I don’t know how I got to it
Answer:
3
Step-by-step explanation:
(40/5)-7+2
PEMDAS says parentheses first, so divide inside the parentheses
(8)-7+2
Then add and subtract from left to right
1 +2
3
Answer:
3
Step-by-step explanation:
Using PEMDAS:
(40/5)-7+2
- > 40/5 - 8
8 - 7 + 2
1 + 2
3
Hope this helps you.
flor ha colocado ¹1/4 kg de papa sobre una balanza . si un cliente le quiere comprar 2 kg de papa , ¿cuantos kilogramos (kg) de papa debe agregar flor sobre l balanza para cumplir con el pedido?
a)3/4 kg de papa
b)¹ 3/4 kg de papa
c1/4 kg de papa
d)¹ 1/4
RAPIDO POR FAVOR E UN EXAMEN SALVEMME LA VIDA
Answer:
a). 3/4 kg de papa
Step-by-step explanation:
Given that,
Patata colocada en balanza = 1 1/4 Kg
Flor de papa total quiere = 2 kg
Encontrar,
Se agregará más peso en la báscula para que sea de 2 kg =?
Procedimiento:
Peso requerido para ser colocado = Peso total - peso colocado
= 2 - [tex]1\frac{1}{4}[/tex]
= 2 - 5/4
= (8 - 5)/4
= 3/4 kg
4x^5/2x^2+5=59
please help
Answer:
[tex]{ \tt{ \frac{4 {x}^{5} }{2 {x}^{2} + 5 } = 59 }}[/tex]
Cross multiply the variables:
[tex]{ \tt{4 {x}^{5} = 59(2 {x}^{2} + 5)}} \\ { \tt{4 {x}^{5} = 118 {x}^{2} + 295}} \\ { \tt{4 {x}^{5} - 118 {x}^{2} = 295}}[/tex]
Factorise the equation:
[tex]{ \tt{ {x}^{2}(4 {x}^{3} - 118) = 295 }}[/tex]
Either x² or ( 4x³ - 118 ) is equal to 295:
For x²:
[tex]{ \tt{ {x}^{2} = 295}} \\ { \tt{first \: answer : \: x =17.2 }}[/tex]
For ( 4x³ - 118 ):
[tex]{ \tt{4 {x}^{3} = 413 }} \\ { \tt{ {x}^{3} = 103.25}} \\ { \tt{second \: answer : \: x = 4.7 }}[/tex]
The legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
show work.
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 +10 ^2 = c^2[/tex]
2. [tex]c^2 = 125[/tex]
3. [tex]c = 5\sqrt{5}[/tex]
Answer:
approximately 11.18 inches or [tex]5\sqrt{5[/tex] inches
Step-by-step explanation:
We have to use Pythagorean Theorem for this problem. a^2 + b^2 = c^2, where c is the hypotenuse and a/b are legs of the right triangle.
5^2 + 10^2 = c^2, 25 + 100 = c^2, 125 = c^2, sqrt125 = c
sqrt125 can be simplified to 5sqrt5 (25 * 5 = 125, sqrt25 = 5)
The hypotenuse is approximately 11.18 inches or [tex]5\sqrt{5[/tex] inches.
4. What is the correct ratio for sin A?
A) 5/12
B) 12/13
C) 5/13
D) 13/12
Answer:
sin A = 12 /13
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin A = opp / hyp
sin A = 12 /13
Please answer only questions 18 and 20 please help me
Answer:
18 is 64 days
20 is 1 37/128
Step-by-step explanation:
I looked it up if I am being completely honest with you but it should be correct
You have to evaluate the question for a and b
Answer:
11
Step-by-step explanation:
a+b^2
Let a=2 and b=3
2+3^2
2 + 9
11
Answer: 11
2 + (3 x 3 )
2 + 9
The required answer would be 11 :)
Step-by-step explanation:
Find the following sums. Please help.
Answer:
5m-n-4p
4a^2+6x-3
Step-by-step explanation:
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
Combine like terms
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
(3-5+7)m +(-4+9-6)n +(7-6-5)p
5m-n-4p
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
Combine like terms
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
(1+1+2)a^2 +(-3+9+0)x +(1-6+2)
4a^2+6x-3
#1
[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]
[tex]\\ \sf\longmapsto 5m-n-4p[/tex]
#2
[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]
[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]
[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]
Which is the pair of congruent right angles?
Answer:
2nd
2nd option <cba=<dea
Answer:
B
as DE=CB
<C=<D
<B= <E
Therefore it is congruent
Have a nice day!
a student says the prime factors of 17 are 1 and 17. is the student correct?
Answer: yes
A prime factor is number that can only divided by itself and one
Since, 17 can only be divided by 17 and 1, the student is correct
Step-by-step explanation:
Find the area of the circle x^2+y^2=16 by the method of intregration
Answer:
Hello,
[tex]16\pi[/tex]
Step-by-step explanation:
[tex]I=\dfrac{Area}{4} =\int\limits^4_0 {\sqrt{16-x^2} } \, dx \\\\Let\ say\ x=4*sin(t),\ dx=4*cos(t) dt\\\\\displaystyle I=\int\limits^\frac{\pi }{2} _0 {4*\sqrt{1-sin^2(t)} }*4*cos(t) \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {cos^2(t)} \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {\frac{1-cos(2t)}{2}} \, dt \\\\=8*[t]^\frac{\pi }{2} _0-[\frac{sin(2t)}{2} ]^\frac{\pi }{2} _0\\\\=4\pi -0\\\\=4\pi\\\\\boxed{Area=4*I=16\pi}\\[/tex]
