Answer:
[tex]a =-3[/tex] [tex]b =2[/tex]
Step-by-step explanation:
Given
[tex]y = ab^x[/tex]
[tex](x_1,y_1) = (0,-3)[/tex]
Required
Find a and b
Substitute [tex](x_1,y_1) = (0,-3)[/tex] for x and y in [tex]y = ab^x[/tex]
[tex]-3 = ab^0[/tex]
[tex]-3 = a * 1[/tex]
[tex]-3 = a[/tex]
Rewrite as:
[tex]a =-3[/tex]
The above implies that (a) is correct;
Hence:
[tex]a =-3[/tex] [tex]b =2[/tex]
So, the equation is:
[tex]y = -3(2)^x[/tex]
Answer: a=-3 b=2
Step-by-step explanation:
he manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is _____. a. significantly less than 3 b. significantly greater than 3.18 c. significantly greater than 3 d. not significantly greater than 3
HELPPPP MEEEE OUTTTT!!!
Answer:
Solution given:
Relationship between base and hypotenuse is given by Cos angle
Cos Angle(?)=base/hypotenuse
Angle{?}=Cos-¹(40/58)
Angle{?}=46°
The indicated angle is 46°
Can someone help me with this math homework please!
Answer:
10
Step-by-step explanation:
f ( 1 ) = 18
First term ( a ) = 18
f ( n + 1 ) = f ( n ) - 2
When, n = 1
f ( 1 + 1 ) = f ( 1 ) - 2
f ( 2 ) = 18 - 2
f ( 2 ) = 16
f ( 2 ) - f ( 1 )
= 16 - 18
= - 2
Common difference ( d ) = - 2
f ( 5 )
= a + 4d
= 18 + 4 ( - 2 )
= 18 - 8
= 10
Dividing with powers of 10
Find the 20th term of the following sequence.
-6, -4,-2, O,...
Step-by-step explanation:
An=-6+(20-1)×2
=-6+19(2)
=-6+38
=32
please help
yuffytdgtutidrysryrdf
Answer:
19 + 1 + 9 + 1
put any of those in the slots
Answer:
19 + 1 + 9 + 1
peace
Now that you know the vertex, find the y-values that pair with a few x-values that are less than 2 and a few that are greater than 2.
Plsssss help!!!!!!!
does anyone know this?
Answer:
The volume is approximately 50 m^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
The radius is 1/2 of the diameter r = 8/2 = 4
V = pi ( 4)^2 (1)
V = 16 pi
Letting pi be approximated by 3.14
V = 3.14 * 16
V = 50.24
The volume is approximately 50 m^3
A parallelogram is cut out of a 12 inch by 8 inch sheet of paper there are four right triangles remnats two have the dimensions 2 inches by 9 inches and the other two have the dimensions 3 inches by 6 inches
Answer:
96 in²
36 in²
60 in²
6.51 in
Step-by-step explanation:
Given that :
Dimension of paper = 12 in by 8 in
Dimension of right triangles :
2 in by 9 in ; 3 in by 6 in
Area of sheet of paper = 12 in * 8 in = 96 in²
Area of triangle = 1/2 base * height
Therefore, area of remnant right triangle :
2 * 1/2 * 2 * 9 = 18 in²
2 * 1/2 * 3 * 6 = 18 in²
Combined area of triangle left = 18in + 18in = 36 in²
Area of parallelogram = Area of sheet - Area of triangles left
Area of parallelogram = 96in² - 36in² = 60 in²
Base, b of parallelogram = 9.22 in
Area of parallelogram = base * altitude,h
60in² = 9.22h
h = 60 / 9.22 = 6.51 in
Anyone knows the answer?
Answer:
a) yes
b) y = -x
c) yes it goes thru the origin (0,0)
Step-by-step explanation:
a) x**2 + y**2 = 17
(-4)**2 + (-1)**2 = 17
16 + 1 = 17 YES
b) the slope of DE is
(y1 - y2)/(x1 - x2)
(-1 -4)/(-4 -1) = -5/-5 = 1, so a perpendicular segment will have a
slope of - 1/current slope or -1.
The midpoint of DE is
x = (x1 + x2)/2 = (-4 +1)/2 = -3/2
y = (y1 + y2)/2 = (-1 +4)/2 = 3/2 so
y = mx + b
y = -x + b plug in the point (-3/2,3/2)
3/2 = -(-3/2) + b
b = 0 SO y = -x
c) The circle equation dictates that it has no offset so centers around the origin (0,0) and the equation of the bisector y = -x indeed fits (0,0).
Write the words that represent s + 21.
Answer:
A number s plus 21
Step-by-step explanation:
s+21
A number s plus 21
A 90 ° angle is divided into 2 angles.
Find the size of the angles.
5x+10 and 6x-41
Answer:
So required ans is 5*11+10=65 6x-41=25
Step-by-step explanation:
You can do as,
5x+10+6x-41=90
11x-31=90
11x=31+90
11x=121
x=121/11
x=11
Factorize the following by splitting the middle term:-
(a) 3x^2 +11x+30
Answer:
See explanation
Question has been corrected
Step-by-step explanation:
Given:
3x² + 11x + 30
To factorise, multiply the coefficient of x² by 30
= 3 * 30
= 90
Find two numbers that have a product of 90 and a sum of 11
** There are no such two numbers, therefore the question can't be solved using factorization
Correcting the error in the question:
x² + 11x + 30
To factorise, multiply the coefficient of x² by 30
= 1 * 30
= 30
Find two numbers that have a product of 30 and a sum of 11
6 and 5
6 + 5 = 11
6 * 5 = 30
x² + 11x + 30
= x² + 6x + 5x + 30
= x(x + 6) + 5(x + 6)
= (x + 6) (x + 5)
Evaluate the function.
f(x) = 4x² + 73 – 18
Find f(-9)
Answer:
379
Step-by-step explanation:
4(-9)²+73-18
4(81)+55
324+55
379
please help with this too
Answer:
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is approximately 125.66 square units
Step-by-step explanation:
The given parameters are;
The radius of the circle with center G, r = 15
The measure of the given angle, m∠AGB = 64°
The area of a sector is given as follows;
Area of a sector of a circle = (θ/360°) × π × r²
Therefore;
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is given as follows;
The area of the sector in circle G = (64°/360°) × π × 15² ≈ 125.66 square units
write 2^60 as an exponent with a base of 16
Recall that 2⁴ = 16. So you have
2⁶⁰ = 2⁴ˣ¹⁵ = (2⁴)¹⁵ = 16¹⁵
Over what interval is the function in this graph constant?
Answer:
hjjjnnnhjjjjj
Step-by-step explanation:
answer is d
6. Which of the following equations has a slope of -2 and passes
through the point (3,-4).
O) y=-2x - 4
O) y=-2x + 2
O) y = -2x+3
O) y = -2x - 1
Answer:
y=-2x+2
Step-by-step explanation:
substitute either the x or y value into the equations, if you substitute x=3 and get back y=-4, the equation is correct
PLEASE I NEED HELP!!
Find the value of x
Answer:
y=4sqrt 3 X=8sqr 3
Step-by-step explanation:
4/y=y/12 y^2=48 y= sqrt 48= sqrt 4 * sqrt 3 * sqrt 4 = y = 4sqrt 3 then X
(4sqrt3)^2+144=x^2
48+144=192
sqrt 192
8sqrt3
If f(x) = -x2 – 1, and
g(x) = x + 5, then
f(g(x)) = [ ? ]x2+[? ]x+[?]
Answer:
-x^2-10x-26
Step-by-step explanation:
f(x) = -x^2 – 1, and
g(x) = x + 5
f(g(x)) = Plug g(x) in for x in f(x)
= -(x+5)^2 -1
= -(x^2 +10x+25) -1
= -x^2 -10x-25 -1
=-x^2-10x-26
The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.
Answer:
[tex]a+b+c=10[/tex]
Step-by-step explanation:
We are given that the graph of the equation:
[tex]y=ax^2+bx+c[/tex]
Passes through the three points (0, 5), (1, 10), and (2, 19).
And we want to find the value of (a + b + c).
First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:
[tex]y=ax^2+bx+5[/tex]
Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:
[tex](10)=a(1)^2+b(1)+5[/tex]
Simplify:
[tex]5=a+b[/tex]
The point (2, 19) tells us that when x = 2, y = 19. Substitute:
[tex](19)=a(2)^2+b(2)+5[/tex]
Simplify:
[tex]14=4a+2b[/tex]
This yields a system of equations:
[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]
Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:
[tex]-10=-2a-2b[/tex]
Add the two equations together:
[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]
Combine like terms:
[tex]4 = 2a[/tex]
Hence:
[tex]a=2[/tex]
Using the first equation:
[tex]5=(2)+b\Rightarrow b=3[/tex]
Therefore, our equation is:
[tex]y=2x^2+3x+5[/tex]
Thus, the value of (a + b + c) will be:
[tex]a+b+c = (2) + (3) + (5) = 10[/tex]
There are nine different marbles in a bag. Supposed you reach in and draw one at a time. And do this three times. How many ways can you draw the three marbles if you do not replace the marble each time
Answer: 504 ways
Step-by-step explanation:
Given
There are nine different marbles in a bag
For the first time, there are 9 possible ways to draw a marble
After removal of first marble, there are 8 possible ways to draw a marble
for the third time, there are 7 possible ways
so, total ways to draw three marble are
[tex]\Rightarrow 9\times 8\times 7=504\ \text{ways}[/tex]
Can you answer this math homework? Please!
and this is right or not
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Answer:
120 kg in morning and 240 kg in afternoon
Step-by-step explanation:
x+2x=360 kg
Work:
x + 2x = 360 kg
3x = 360 kg
3x/3 = 360 kg/3
x = 120
2x=2(120 kg) =240 kg
Final Answer:
So, 120 kg in morning and 240 kg in the afternoon.
Hope this helps!
Who know how to do this??
Answer:
Step-by-step explanation:
With some research I found that the medians (QK, RJ, and SI) are broken into 2:1 ratios.
So what this means is that QD is twice as long as DK.
QD = 2DK
QD = 2 * 6.5
QD = 13
(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd) =
Answer:
4c² + 11cd + 5d
Step-by-step explanation:
(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)
-4c² + 7cd + 8d - 3d + 8c² + 4cd (opening bracket)
8c²-4c²+7cd + 4cd + 8d - 3d
= 4c² + 11cd + 5d
Consider two parabolas: One has equation 1 ( 4)( 4) 2 y x x =−+ . The other has the same xintercepts, but goes through the point (2,−12) How far apart are the vertices of the two parabolas
Answer:
Following are the responses to the given question:
Step-by-step explanation:
[tex]\to y=(\frac{1}{2})(x-4)(x+4)\\\\\to y=(\frac{1}{2}) (x^2-16)\\\\\to y=(\frac{1}{2})(x-0)^2-8\\\\vertex \to (0,-8)[/tex]
The general x-intercept parabola equation [tex]y=k(x-4)(x+4)[/tex]
Parabola crosses the dot (2,-12)
[tex]\to k(2-4)(2+4)=-12\\\\\to k(-2)(6)=-12\\\\\to -12k=-12\\\\\to k=\frac{-12}{-12}\\\\\to k=1[/tex]
The parabolic equation which crosses the position [tex](2,-12)[/tex] is[tex]y=(x-4)(x+4)[/tex]
[tex]\to y=(x-4)(x+4)\\\\\to y=x^2-16\\\\\to y=(x-0)^2-16\\\\vertex \to (0,-16)[/tex]
The distance among the vertices of the two parabolas:
[tex]= \sqrt{(0 - 0)^2+(-8-(-16))^2}\\\\ = \sqrt{0+(-8+16))^2}\\\\ =\sqrt{0+(8)^2}\\\\=\sqrt{(8)^2}\\\\= 8\\\\[/tex]
simplify
(−5abc − 6ac + 7cb) − (10abc + 6ac − 8bc)
Answer:
-15abc - 12ac + 15bc
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(-5abc - 6ac + 7cb) - (10abc + 6ac - 8bc)
Step 2: Simplify
[Distributive Property] Distribute negative: -5abc - 6ac + 7cb - 10abc - 6ac + 8bcCombine like terms: -15abc - 12ac + 15bc
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = x³ – 6x² – 11x + k
Factor => x + 2
Value of k =?Next, we shall obtained the value of x from x + 2. This can be obtained as follow:
x + 2 = 0
Collect like terms
x = 0 – 2
x = –2Finally, we shall determine the the value of k. This can be obtained as illustrated below:
f(x) = x³ – 6x² – 11x + k
x = –2
Value of k =?f(–2) = 0 since x + 2 is a factor
x³ – 6x² – 11x + k = 0
(–2)³ – (–2)² – 11(–2) + k = 0
–8 – (4) + 22 + K = 0
–8 – 4 + 22 + K = 0
10 + k = 0
Collect like terms
k = 0 – 10
k = –10Therefore, the value of k is –10
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