Answer:
60
Step-by-step explanation:
The initial y value can be found by setting x to 0. Anything to the power of 0 is 1, so 1.71^x when x is 0 is just 1. 60*1=60, which is the initial y value. Hope this helps!
The initial amount 'y' of the exponential function [tex]y = 60(1.71)^x[/tex] is 60. This value represents the function's y-intercept, the amount present before any exponential growth occurs.
The student has provided an exponential function and wishes to know the initial amount, which can be expressed as 'y' in the function [tex]y = 60(1.71)^x[/tex]. The initial amount when x=0 is the coefficient of the exponential term. For this function, when x equals 0,[tex](1.71)^0[/tex] is 1, since any number raised to the power of 0 is 1. Therefore, the initial amount or the y-intercept of this function is 60.
This value represents the starting quantity before any growth (or decay if the base were less than 1) has occurred in the context of the function. It is important to note that the base of the exponential function (1.71 in this case) indicates the rate of growth per unit increase of the variable x
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Answer: part of the alphabet
Step-by-step explanation: nice
A picture frame measures 9 inches high and 5.4 Inches wide. It will be proportionately enlarged so the height will be 15 inches. How wide will the frame be?
Answer:
Width: 9 inches
Step-by-step explanation:
1. We can see that the height increased by 6 inches, provided a difference of 15 and 9. If the question states that the frame's dimensions were proportionately enlarged, perhaps the height's enlargment could be benificial
2. If we were to take a ratio where the increased height is over the previous height (height enlargment/prior height) that would be 6/9, or in other words, can be simplified to be 2/3
3. We can see that if the width were to be enlarged, we might be able to determine how much it should be enlarged through a proportionality, provided the frame's dimensions are proportionately enlarged. Now if x ⇒ the width enlargment: 2 / 3 = x / 5.4
4. Through cross multiplication, let us solve for x:
2 * 5.4 = 3 * x,
10.8 = 3 * x,
x = 3.6 inches by which the width should be enlarged
5. If we are to determine the new width of the frame after enlargment, add 5.4 to 3.6 ⇒ the width of the frame ⇒ 9 inches
Study the following diagram, where points C and D lie on circle A.
Point B lies in the exterior of circle A.
Angle ACB and angle ADB are right angles.
The diagram as described in the problem, where segment B C equals negative 2 x plus 85 and segment B D equals 5 x minus 48.
What is the length of BC¯¯¯¯¯¯¯¯?
Enter the correct value.
Answer:
Triangle ACB = Triangle ADB
=> BC = BD
=> -2x+85 = 5x - 48
=> x = 133/7 = 19
=> BC = -2 x 19 + 85 = 47
If we are provided with the value of AC or CD, we can calculate the length of BC is 47
Let's first determine the lengths of segment BC and BD in terms of x using the given expressions:
BC (B C¯¯¯¯¯¯¯¯) = -2x + 85
BD (B D¯¯¯¯¯¯¯¯) = 5x - 48
Now, as ACB and ADB are right angles, we can utilize the property of perpendicular chords intersecting a circle to find the value of x. When two chords intersect inside a circle, the product of their segments is equal. Therefore, we can set up the following equation:
BC * BD = (AC * CD) [Property of perpendicular chords intersecting]
Substitute the values:
=> BC = BD
When we simplify this one, then we get,
-2x+85 = 5x - 48
Then the value of x is calculated as,
x = 133/7 = 19
BC = -2 (19) + 85 = 47
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An equation for the depreciation of a car is given by y = A(1-r)^twhere y = current value of the car, A = original cost, r = rate of
depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately
how old is the car?
Answer: The car is 6.6 years old.
Step-by-step explanation:
Hi, to answer this question we have to replace the values in the equation given:
Y = 1/2 (half the value)
A = 1 (total value)
r =10% = 0.10 (decimal form)
Replacing:
y = A(1-r)^t
1/2 = 1 (1-0.10)^t
Solving for t:
(1/2)/1 = 0.9^t
1/2 = 0.9^t
log 1/2 = log 0.9^t
log 1/2 = (t) log 0.9
(log 1/2)/ log 0.9 = t
6.57 =t
6.6 years (rounded)
can someone please help i need to write the equation of the green line
f(x) = ax + b
(0, -4):
f(0) = a•0 + b
f(0) = b ⇒ b = -4
(12, 0):
0 = a•12 + b
0 = 12a - 4
4 = 12a
[tex]a=\frac4{12}=\frac13[/tex]
The equation of the green line:
[tex]\underline{\,y=\frac13x-4\,}[/tex]
or: [tex]y=\frac13x-4[/tex]
[tex]-\frac13x+y+4=0\\\\\underline{x-3y-12=0}[/tex]
Plz help meeeee plzzzz
Answer:
-4p³+3p²-17p
Step-by-step explanation:
(-3p³+5p²-2p)+(-p³-8p²-15p)
-3p³+5p²-2p-p³-8p²-15p
-3p³-p³+5p²-8p²-2p-15p
=-4p³+3p²-17p
If you had 20 equal parts, how would you shade in 85% of it? How many parts would you shade in?
Shade in 17 parts. 100% is 20 parts, and 100/20=5. You have to shade 85%, and 85/5=17.
Shade in 17 parts.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, we have,
We had 20 equal parts.
i.e. 100% is 20 parts,
and 100/20=5.
You have to shade 85%,
and 85/5=17.
Hence, there are Shade in 17 parts.
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I need some help with this answer please :)
Answer:
1/9 is my guess
Step-by-step explanation:
Factor polynomial p^2-20p+100
Answer:
[tex](p-10)^2[/tex]
Step-by-step explanation:
[tex]p^2-20p+100=\\(p-10)^2[/tex]
Hope this helps!
p − 10 ) 2
Step-by-step explanation:
What is the surface area of a conical grain storage tank that has a height of 62 meters and a diameter of 24 meters? Round the answer to the nearest square meter.
2,381 m2
2,790 m2
2,833 m2
6,571 m2
NEED HELP ASAP
the angle of elevation from the far side of the pool to the top of the waterfall is 54 degrees and the distance is 230 ft. Find x
Answer:
(Use right triangle)
1) find the height of the waterfall (opposite side) to the nearest foot.
draw the triangle. distance from far side of the pool to the top of the waterfall is the hypotenuse given to be 230.
sinx = opp/hyp
sin54 = opp/230
opp = 230sin54
opp = approx 186 ft
2) find the width across the pool (adjacent side) to the nearest foot.
cosx = adj/hyp
cos54 = adj/230
adj = 230cos54
adj = approx 135 ft
Answer: 135 ft
The value of x is 135.2 feet.
To understand more, check below explanation.
Angle of elevation:From given figure,
It is observed taht, a right angle triangle is formed in the given figure.
Angle of elevation = 54 degree
Hypotenuse = 230 feet
We have to find base i.e x
Apply cosine of angle,
[tex]cos (54)=\frac{x}{230}\\ \\x=230*cos(54)\\\\x=230*0.587\\\\x=135.2ft[/tex]
Hence, the value of x is 135.2 feet.
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The diameter of a golf ball is about 4 centimeters. Which of these is the closest to the volume of a golf ball?
16.75 cm^3
33.51 cm^3
100.53 cm^3
268.08cm^3
The volume is approximately 33.51 [tex]cm^3[/tex], option B.
The question asks us to determine the closest volume to a golf ball with a diameter of approximately 4 centimeters. To find the volume of a sphere (which is the shape of a golf ball), we use the formula:
V = (4/3)π[tex]r^3[/tex],
where r is the radius of the sphere. Since the diameter of the golf ball is given as 4 cm, the radius would be half of that, which is 2 cm. Plugging in the radius into the formula, we have:
[tex]V = (4/3)\pi(2 cm)^3 = (4/3)\pi(8 cm^3) = (32/3)\pi cm^3,[/tex]
Now, we calculate the value using the approximation π = 3.14:
V = (32/3) × 3.14 [tex]cm^3[/tex] = 33.51 [tex]cm^3[/tex] (approximately).
Therefore, the volume that is closest to the actual volume of the golf ball is 33.51 [tex]cm^3[/tex], option B.
pls pls pls pls help ;(
Answer the problem below. Show all your work/thinking.
1. Find the surface area of the following figure, then explain the steps of your solution in
paragraph form.
Answer:
Around 202.08
Step-by-step explanation:
The formula for the surface area of a pyramid is [tex]a^2 +2a\sqrt{\frac{a^2}{4}+h^2}=9^2+2\cdot 9\sqrt{\frac{9\cdot 9}{4}+5^2}=81+18\sqrt{45.25}\approx 202.08[/tex]. Hope this helps!
For which value of x would this model make the least sense
to use? A.-2.75 B.0.25 C.1.75 D.2.25
Answer: A
Explanation: x is your independent variable and is time, so it is unlikely to have negative amounts of time.
The time will be 2.25 seconds. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
h(x) = – 16x² + 100
Where x is the time in seconds and h(x) is the height at x.
Let the height is y feet.
Then the value of y will be
y = 84 – 65
y = 19 feet
Then the time will be
19 = – 16x² + 100
16x² = 100 – 19
16x² = 81
4x = 9
x = 2.25 seconds
Then the correct option is D.
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solve for c 3c − 10 = 2c
Answer:
10 is your answer for c.
Step-by-step explanation:
Isolate the variable c. Note the equal sign, what you do to one side, you do to the other.
Subtract 3c from both sides:
3c (-3c) - 10 = 2c (-3c)
-10 = 2c - 3c
-10 = -c
Isolate the variable, c. Divide -1 from both sides:
(-c)/-1 = (-10)/-1
c = -10/-1
c = 10
c = 10 is your answer.
~
The sum of the first 333 terms of a geometric series is 171171171 and the common ratio is \dfrac23
3
2
start fraction, 2, divided by, 3, end fraction.
What is the first term of the series?
Answer:
The first term of the series is 81
Step-by-step explanation:
The sum of the nth term of a geometric sequence is expressed as shown;
Sn = a(1-rⁿ)/1-r for r<1
a is the first term
r is the common ratio
n is the number of terms
Given Sn = 171
r = 2/3
n = 3
a =?
Substituting the values in the equation
171 = a(1-(2/3)³)/1-2/3
171 = a(1-8/27)/(1/3)
171 = a(19/27)/(1/3)
171 = a × 19/27 × 3/1
171 = a × 19/9
Cross multiplying
171×9 = 19a
1539 = 19a
a = 1539/19
a = 81
The first term is 81
Answer:
81
Step-by-step explanation:
Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the
following two cities whose latitudes are given. You may assume that these cities are on
the same basic longitude.
Cincinnati, Ohio (39° 8' 46" N) and Huntsville, Alabama (34° 43'41" N)
Answer:
308.44 miles
Step-by-step explanation:
Cincinnati, Ohio (39° 8' 46" N); and Huntsville, Alabama (34° 43'41" N)If the two locations are on the same basic longitude, then they are both on a great circle.
Distance along great circle [tex]=\dfrac{\theta}{360^\circ}X2\pi R[/tex]
Where:
[tex]\theta=$Angular difference\\R=Radius of the earth[/tex]
Since they are on the same polar axis (North), we subtract.
Angular Difference =39° 8' 46"-34° 43'41"=4°25'5"
Therefore:
[tex]Distance =\dfrac{4\°25'5''}{360^\circ}X2*4000*\pi \\=308.44 \:miles[/tex]
Need help with question 2 ASAP PLS anything is appreciated:)
Answer:
D
Step-by-step explanation:
It is D because the coordinate (1,1) isn't equals to (2,4); (3,27); or (4,24). It is not constant and you cannot make a linear function/equation out of it.
risha wants to buy a computer for $775. She already has $275 saved and earns $100 a week babysitting. a. Use w to represent weeks and write an inequality that could be used to determine how many weeks she would have to work to afford the computer. b. How many weeks does she have to work?
Answer
Inequality=100x+275≥775 Answer=5 or more
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Solve the inequality:
10x - 3 ≥ 2
A. x ≤ 1/2
B. x ≤ 2
C. x ≥ 1/2
D. x ≥ 2
10x−3+3≥2+3
10x≥5
(10x10)/2≥(5/10)
x≥1/2
5)What will be the new position of the given point (7,4) after translation of
2 units left and 4 units up?
a) (5,8) b) (9,-8) c) (5,-8) d) (9,8)
Answer:
The correct answer is (5,8)
Step-by-step explanation:
On which of the following lines does the point (–3, –1) lie? y = −4x − 6 y = 3x + 9 y = −3x − 10 y = 5x − 1
Answer: [tex]y = -3x - 10[/tex]
Step-by-step explanation:
You can substitute the value "-3" for x and "-1" for y in each of the equations given. Whichever equation is correct when simplified is the line that the point (-3, -1) lies on:
[tex]-1 = -4(-3)-6\\\\-1=3(-3)+9\\\\-1=-3(-3)-10\\\\-1=5(-3)-1[/tex]
Simplifying the right side of each equation:
First equation: -1 = 6
Second equation: -1 = 0
Third equation: -1 = -1
Fourth equation: -1 = -16
The correct answer is "[tex]y = -3x - 10[/tex]".
Howard wants to use multiplication to solve w=5 divided by 1/5 Which multiplication equation can Howard use?
A:5*1/5=w
B:1/5*5=w
C:5=1/5*w
Answer:
C.5=1/5*w
Step-by-step explanation:
W=5÷1/5
Multiply both sides by 1/5
(1/5)w=5÷1/5(1/5)
(1/5)w=5×5/1(1/5)
1/5*w=25/1 * 1/5
1/5*w=25/5
1/5*w=5
It can also be written as
5=1/5*w
Answer:
5 1/5 * w
Step-by-step explanation:
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HELP ME please :) Please
Answer:
If the question was to the first one I'm pretty sure the answer is a lot fewer people got sick I'm not sure but the second question but from what I could see of the bottom question burning fossil fuels driving cars and deforestation I know are may cause global warming I can't see the rest of it though and I'm not sure about ice cores
Step-by-step explanation:
2/3+q=1/2 what is Q
Q=rational number=1/6
2/3+q=1/2=1/6
Which set of ordered pairs represents y as a function of x? A) {(0, 0), (−1, 2), (−1, −2), (−2, 4), (−2, −4)} B) {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)} C) {(0, 0), (0, 1), (0, 2), (0, −1), (0, −2)} D) {(0, 0), (−1, −0.5), (−2, −1), (−3, −1.5), (−4, −2)}
Answer: D
Step-by-step explanation:
No two coordinates can have to same input(x) and different outputs(y)
Option A represents y as a function of x because each x-value is associated with only one y-value.
Explanation:To determine if a set of ordered pairs represents y as a function of x, we need to check if each x-value is associated with a unique y-value. In option B) {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)}, we can see that the x-value 3 is associated with two different y-values, 9 and 16. Therefore, option B) does not represent y as a function of x.
The correct answer is option A) {(0, 0), (-1, 2), (-1, -2), (-2, 4), (-2, -4)}. In this set, each x-value is associated with only one y-value. For example, x = -1 is associated with y = 2 and y = -2. Since no x-value is repeated with different y-values, this set represents y as a function of x.
Option C) {(0, 0), (0, 1), (0, 2), (0, -1), (0, -2)} and option D) {(0, 0), (-1, -0.5), (-2, -1), (-3, -1.5), (-4, -2)} both have repeated x-values with different y-values, so they do not represent y as a function of x.
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Which function has a domain of all real numbers
Functions with all real numbers as their domain include polynomial functions, sine and cosine functions, and exponential functions. For example, the function f(x)=x², f(x) = sin(x), or f(x) = cos(x) and f(x)=a^x (where a>0).
Explanation:In Mathematics, the domain of a function is the set of values that can be plugged into the function. There are multiple functions that have a domain of all real numbers, some of them are polynomial functions, sine and cosine functions, and exponential functions.
For example, the function f(x)=x² is a polynomial function where any real number can be inputted for x, hence its domain is set of all real numbers.
Similarly, sine and cosine functions, represented as f(x) = sin(x) or f(x) = cos(x), have a domain of all real numbers, because sine and cosine are periodic and their values repeat over every interval of 2π.
Furthermore, the exponential functions, represented in the form f(x)=a^x (where a>0), have also their domains as the set of all real numbers.
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An amusement park's cost for cotton candy is $1.50. The markup rate for cotton candy is
300%. What is the price of cotton candy at the park?
Answer:
The answer is $6
Hope this helps!
The price of cotton candy at the park is $6.00.
The markup rate of 300% means the price is increased by three times the cost. So, $1.50 * 3 = $4.50 is the markup cost. Adding the original cost to the markup cost gives $1.50 + $4.50 = $6.00.
Are these triangles similar?
Answer:
no
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
They are not similar because one has a length of 9 and one has a length of 16They would be similar if it had a side length of 8 and a bottom lenght of 6Hope this helped :)Plz help me love you
Answers)
27=6
30=82
33=24