The exponential function h(x) =3^x +4 is a growth function
The function's y-intercept is located at (0,5), and the function is true for all real values of x
How to determine the true statement?The function is given as:
h(x) =3^x +4
Set x to 0
h(0) =3^0 +4
h(0) = 5
The above means that the function's y-intercept is located at (0,5)
Also, the function is true for all real values of x
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Evaluate 9x^2y^−2 for x = –3 and y = 2.
a)9(−6)^0
b)1/144
c)20 1/4
d)324
Answer:
c)20 1/4
Step-by-step explanation:
[tex]9x^{2}y^{-2}[/tex]
If We replace x by -3 and y by 2 we get :
[tex]9\left( -3\right)^{2} \left( 2\right)^{-2}[/tex]
Or we have :
[tex]\left( -3\right)^{2} =9\ \text{and} \ \left( 2\right)^{-2} =\frac{1}{2^{2}} =\frac{1}{4}[/tex]
then
[tex]9\left( -3\right)^{2} \left( 2\right)^{-2}=9\times9\times\frac{1}{4} = \frac{81}{4}[/tex]
on the other hand :
[tex]\frac{81}{4} =\frac{80+1}{4} =\frac{80}{4} +\frac{1}{4} =20+\frac{1}{4}=20\frac{1}{4}[/tex]
What will a $140,000 house cost 7 years from now if the price appreciation for homes over that period averages 7% compounded annually?
The future cost of the house will be $___
(Round to the nearest cent as needed.)
The house will cost approximately $246,359.85 seven years from now.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
In this problem,
P = $140,000
r = 0.07
n = 1 (compounded annually)
t = 7.
Plugging in these values.
A = $140,000 (1 + 0.07/1)^(1 x 7)
A = $140,000 (1.07)^7
A = $246,359.85
Therefore,
The house will cost approximately $246,359.85 seven years from now.
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455 rounded to the nearest ten
Answer:
it's 460 I think, because the last number is a five so if it's over a five you round up
could yall help me on this pls!!
Answer:
Step-by-step explanation:
Remark
Make a very crude diagram of what these points look like. You will find that
(-8,6) is above (-8,3) (-3,6) is above (-3,3)That gives you a hint about how to find the Length and width.
Givens
From (-8,-3) and (-3, 3) L = -8 - -3 = - 5
From (-8,6) and (-8,3) w = 6 - 3 = 3
Solution
The length cannot be minus 5. The way to get around that is to call it and absolute value of (-5) which is 5
So the area = L*W
area = 5 *3
area = 15
Answer
Area = 15
Vectors U and V are shown on the graph (The graph with letters U and V)
Which of the following vectors represents u-v
Answer:
see attached
Step-by-step explanation:
The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.
__
This sum is shown in the attachment.
A bicycle store costs $2700 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $70. How many bicycles must the store sell each month to
The store must set bicycles each month to break even
Write an equation for a line that passes through points (-6, 1), (1, 4), (5, 6)
Answer:
y= .45x + 11/3
Step-by-step explanation:
Those points are not on the same line but you can get pretty close with
y= .45x + 11/3
5 power 2x = 1/125. find the value of x.
Answer:
x = -3/2
Step-by-step explanation:
note: 1/125 can be written as 5 exponent -3 thus, 5^-3
Expressing it in this form, we can rewrite the above equation as
5^2x = 5^-3
As part of the laws of indices and logarithms, when the bases are the same and they are equating, You equate only the exponents
therefore, we have;
2x = -3
divide through by 2
x = -3/2
What is the volume of a right cylinder
with a radius of 14 units and a height
of 31 units?
Answer:
6076π ≈ 19088.3 cubic units
Step-by-step explanation:
The volume of a cylinder is found using the formula ...
V = πr²h
__
For the given dimensions, the volume is ...
V = π(14²)(31) = 6076π ≈ 19088.3 . . . cubic units
Use the graph of the function to find, 4-6).
Answer:
D. 3Step-by-step explanation:
f(-6) is the corresponding number of -6 and you can spot it on the y-axis
A package of 6 pencils costs $3. The cost per pencil is $.
Answer:
Each pencil costs 50 cents
Step-by-step explanation:
Step 1: Determine the price per unit
(Price of Items) / (Amount of items)
($3) / (6)
$0.5
Answer: Each pencil costs 50 cents
ANSWERS FOR THESE TWO!!
Answer:
x = 4 or x = -3
-1
Step-by-step explanation:
26.
x² = x + 12
x² - x - 12 = 0
(x - 4)(x + 3) = 0
x - 4 = 0 or x + 3 = 0
x = 4 or x = -3
27.
(-6 + 4)/2 = -2/2 = -1
anyone know the answer?
Answer:
31.53 cm[tex] \: [/tex]
Step-by-step explanation:
It is given that, The circumference of a circle is 198 cm and we are to find the radius of the circle.
[tex] \: [/tex]
To find the radius of the circle we must know this formula first :
[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: 2 \pi r \: =Circumference_{(circle)}}}}}}} \: \: \bigstar \\ \\ [/tex]
Now substituting the values in the formula :
[tex]\\{ \longrightarrow \qquad{ {{ \tt{ \: 2 \times 3.14 \times r \: =198}}}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ {{ \tt{ \: 6.28 \times r \: =198}}}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ {{ \tt{ r \: = \frac{198}{6.28} }}}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \pmb {{ \frak{ r \: = 31.528 }}}}} \\ \\ [/tex]
Therefore,
The radius of the circle is 31.53 cm (Rounded to nearest hundredth)I need help on number 9
Answer:
3. -1/3 ± 2i√5 / 3
Step-by-step explanation:
3x^2 + 2x = -7
Divide through by 3:
x^2 + 2/3 x = -7/3
Completing the square:
x^2 + 2/3 x + (1/3)^2 = -7/3 + (1/3)^2
(x + 1/3)^2 = -7/3 + 1/9
(x + 1/3)^2 = -20/9
x + 1/3 = ±√(-20) / 3
x + 1/3 = ± 2√-5/3
x = -1/3 ± 2i√5 / 3
please help! thank you!
Step-by-step explanation:
p(p-q) - q(q-p)
p²-pq - q² +pq
p² - q²
Choice 1
When the graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L, the volume obtained depends on L. What value of L minimizes the volume in part (c)?
The value in the part (c) is 1/(b-a) if the graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L, the volume obtained depends on L.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L.
For part(c)
[tex]\rm V(L) = \int\limits^b_a {\pi(f(x) -L)^2} \, dx\\\\\rm V(L) = \int\limits^b_a {\pi((f(x))^2 -2f(x)+L^2)} \, dx\\\\\rm V(L) = \pi \int\limits^b_a {(f(x))^2} \, dx-2\pi L \int\limits^b_a {f(x)} \, dx +L^2\pi\int\limits^b_a {} \, dx[/tex]
Now finding V'(L)
[tex]\rm V'(L) = -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L \int\limits^b_a {} \, dx[/tex]
[tex]\rm V'(L) = -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L (b-a)[/tex]
Now equation V'(L) to zero; V'(L) = 0
[tex]\rm -2\pi \int\limits^b_a {f(x)} \, dx+2\pi L (b-a)=0[/tex]
[tex]\rm \int\limits^b_a {f(x)} \, dx= L (b-a)[/tex]
[tex]\rm L = \frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex]
The above expression is representing the critical point.
Now finding V''(L)
V''(L) = 2π(b-a) >0 at L
[tex]\rm L = \frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex] (minimizines the volume)
Thus, the value in the part (c) is 1/(b-a) if the graph of any continuous function y = f(x) for a ≤ x ≤ b is rotated about the horizontal line y = L, the volume obtained depends on L.
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PLEASE HELP
Bobby invests $2500 and wants it to grow to $5000, what interest rate will double your money in 5 years? (round to nearest tenth - one decimal space)
Answer:
14.9 %
Step-by-step explanation:
2 = double
2 = ( 1+ i)^5 i = interest in decimal 5 = years
i = .149 = 14.9 %
What is the radius of a circle that has a circumference of 3.14 meters?
circumference= 3.14m
to find:the radius of the circle
solution:Circumference of a circle = 2πr
Given, circumference = 3.14 meters
Therefore:
2πr = Circumference of a circle
2πr = 3.14
2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14]
6.28r = 3.14
r = 3.14/6.28
r = 0.5
Use your line of best fit from question 5 to find the approximate value of y when x equals 24
The line of best fit is an illustration of a linear regression
Using the assumed parameters, the value of x when x = 24 is 30.75
How to determine the value of y?The equation of the line of best fit is not given, and the parameters to calculate the line of best fit are missing.
So, I will assume the following parameter values.
Assume that the line of best fit passes through the points
(x,y) = (1,2) and (5,7)
The slope of the line would be:
m = (7 - 2)/(5- 1)
m = 1.25
The equation is then calculated as:
y =m(x - x1) + y1
This gives
y = 1.25(x - 1) + 2
Expand
y = 1.25x - 1.25 + 2
Evaluate
y = 1.25x + 0.75
When x = 24, we have:
y = 1.25 * 24 + 0.75
Evaluate
y = 30.75
Using the assumed values, the value of x when x = 24 is 30.75
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proportionality of triangles- setup and solve
How could you have simplified this problem in 2 different ways
[tex]( 7 . 3^{6} ) ^{4}[/tex]Answer:
= [tex](7^{-3--2}[/tex] x [tex]3^{-8--2} ) ^{-4}[/tex]
= [tex](7^{-1}[/tex] x [tex]3^{-6}) ^{-4}[/tex]
= [tex]( 7^{1}[/tex] x [tex]3^{6}) ^{4}[/tex]
= [tex]7^{4}[/tex] x [tex]3^{24}[/tex]
OR
= [tex](\frac{3^{-8} }{7 . 3^{-2} }) ^{-4}[/tex]
= [tex](\frac{1}{7 . 3^{6} } ) ^{-4}[/tex]
= [tex]( 7 . 3^{6} ) ^{4}[/tex]
= [tex]7^{4}[/tex] x [tex]3^{24}[/tex]
Step-by-step explanation:
Select the correct answer.
Rewrite the following expression.
The difference 11/14 - 2/10
Answer:
11/14-2/10=41/70=0.58
Please help me 50 points!!!!!
Answer:
1 trapezoid
2 triangle
3 rectangle
What is the surface area of this right prism?
1050 in²
1200 in²
1440 in²
1800 in²
Answer:
The anwer is B 1200 in
Step-by-step explanation:
I'm stuck on this one! Please help
Answer:
The answer is 12
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
Option B will be the best option.
Identify the polynomial that is the difference of two squares.
A. 25m2 − 16n
B. 49m2 − 81n4
C. 36m2 − 8n8
D. 9m2 − 5n6
Answer:
Option B, [tex]49m^2 - 81n^4[/tex]
Step-by-step explanation:
Step 1: Determine the difference of two squares
According to online, "In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra." a^2 - b^2 gives us (a + b)(a - b)
The only one that would work is Option B so lets factor it out.
[tex]49m^2 - 81n^4[/tex]
[tex](7m + 9n^2)(7m - 9n^2)[/tex]
Answer: Option B, [tex]49m^2 - 81n^4[/tex]
Help help help math math
Answer:
-6x-10
Step-by-step explanation:
you multiply 3x by -2
and 5 by -2
never forget the negative
Eddie's dog weighs 31.8 kilograms. How many grams are equivalent to 31.8 kilograms?
A: 0318 grams
B: 318 grams
C: 3,180 grams
D: 31,800 grams
Answer:
D
Step-by-step explanation:
to find the value in grams, we just multiply by a 1000
so, 31.8 × 1000 = 31,800 grams
Can somebody help me round 376.77 to the nearest whole. With steps (guidance)
It would totally help me with the state exam tomorrow!
Answer:
To round 376.77 to the nearest dollar consider the tenths’ value of 376.77, which is 7 and equal or more than 5. Therefore, we have to round the amount up: the dollar part of 376.77, 376, increases by 1 to 377, and the decimal point and all digits (.77) are removed.
Step-by-step explanation: