Answer:
The answer is C. y=cos(0.4x)
Step-by-step explanation:
took the test
Answer: c
Step-by-step explanation:
y=cos(0.4x)
Find the sum and the difference of the following expressions.
a-b and a+b
The sum is_____, The difference is_____.
Answer:
sum=2a
diff.=-2b
Step-by-step explanation:
a-b+a+b=
2a
a-b-a-b=-2b
the population P of a bacteria culture is modeled by P=4300e^kt, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double?
Answer:
93 h
Step-by-step explanation:
P = 4300eᵏᵗ
1. Calculate the value of k
lnP = ln4300 + kt
ln5800 = ln4300 + k(40 h)
8.666 = 8.366 + 40k h
8.666 - 8.366 = 40k h
0.299 = 40 k h
k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹
2. Calculate the time for the population to double
2 × 4300 = 4300eᵏᵗ
2 = eᵏᵗ
ln2 = kt
t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h
It takes 93 h for the population to double.
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y= 8/sqareroot of 2x+4
f(x) = 8, g(x) = square root of quantity two x plus four.
f(x) = square root of quantity two x plus four., g(x) = 8
f(x) = eight divided by x., g(x) = 2x + 4
f(x) = eight divided by square root of x., g(x) = 2x + 4
Answer:
The fourth option gives the result.
Step-by-step explanation:
We have to find f(x) and g(x) from options given such that y = f[g(x)] is equivalent to [tex]y = \frac{8}{\sqrt{2x + 4}}[/tex].
Here, the fourth option gives the result.
If [tex]f(x) = \frac{8}{\sqrt{x} }[/tex] and g(x) = 2x + 4, then the composite function [tex]f[g(x)] = \frac{8}{\sqrt{2x + 4}}[/tex]
⇒ [tex] y = \frac{8}{\sqrt{2x + 4}}[/tex] ( Answer )
3. What is the solution to 3x2+3x+5=0? (7 point)
mm -
Cm 2COO
-3+1V17
3
31151
6
-1£i17
2
-3ti51
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x^2+3x+5 = 0[/tex]
We will use the quadratic formula for solving the given equation
The quadratic formula is:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ ,\ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Here,
a = 3
b = 3
c = 5
[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]
As we know
[tex]i = \sqrt{-1}[/tex]
So,
[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Hence,
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Keywords: Quadratic equation, quadratic formula
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Stuck on this please help
Answer:
The answers are given below.
Step-by-step explanation:
7. Simplified Fractions/Integers:
a. [tex]$ (25)^{\frac{-3}{2}} $[/tex]
= [tex]$ (5^2)^{\frac{-3}{2}} $[/tex]
= [tex]$ 5^{-3} $[/tex]
= [tex]$ \frac{1}{5^3} = \frac{1}{125} $[/tex] is the required answer.
b. [tex]$ \bigg ( \frac{1}{7} \bigg )^{2} $[/tex]
= [tex]$ \bigg( \frac{1}{7^2} \bigg) $[/tex]
= [tex]$ \frac{1}{49} $[/tex] is the required answer.
c. [tex]$ \bigg ( \frac{1}{7} \bigg) ^{-3} $[/tex]
= [tex]$ \bigg ( \frac{1}{7^{-3}} \bigg )$[/tex]
= [tex]$ 7^{3} $[/tex] = 343 is the required answer.
8. Simplified Fractions:
a. [tex]$ \bigg( \frac{27}{8} \bigg ) ^{\frac{2}{3}}$[/tex]
= [tex]$ \bigg ( \frac{3^3}{2^3} \bigg ) ^{\frac{2}{3}} $[/tex]
= [tex]$ \bigg ( \frac{3}{2} \bigg) ^2 $[/tex]
[tex]$ = \frac{9}{4} $[/tex] is the required answer.
b. [tex]$ \bigg ( \frac{4}{25} \bigg)^{\frac{-3}{2}} $[/tex]
= [tex]$ \bigg ( \frac{2^2}{5^2} \bigg)^{\frac{-3}{2}}[/tex]
= [tex]$ \bigg ( \frac{2^{-3}}{5^{-3}} \bigg ) $[/tex]
= [tex]$ \bigg( \frac{5^3}{2^3} \bigg ) $[/tex]
= [tex]$ \frac{125}{8} $[/tex] is the required answer.
9. Index Forms:
a. √3
= [tex]$ 3^{\frac{1}{2}} $[/tex] is the required answer.
b. ∛3
= [tex]$ 3^{\frac{1}{3}} $[/tex] is the required answer.
c. [tex]$\sqrt[6]{2} $[/tex]
= [tex]$ 2^{\frac{1}{6} $[/tex] is the required answer.
d. [tex]$ \sqrt{5^3} $[/tex]
= [tex]$ 5^{\frac{3}{2}} $[/tex] is the required answer.
e. [tex]$ \frac{1}{(\sqrt[3]{5})^2} $[/tex]
= [tex]$ \frac{1}{5^{\frac{2}{3}}} $[/tex]
= [tex]$ 5^{\frac{-2}{3}} $[/tex] is the required answer.
Angeline made a dish with 5 1/3 cups of pasta. One serving is 0.2 cups. How many servings of pasta were in the dish Angeline made?
Answer:
26 2/3
Step-by-step explanation:
We could turn both of these numbers into decimals, but I find fractions easier.
so 5 1/3 as an improper fraction is 16/3
0.2 as a fraction is 2/10 or 1/5
so now we have the equation 16/3 ÷ 1/5 or 16/3 x 5/1
this give me 80/3, then when simplified gives me 26 2/3.
Leah has 280 toy cars she puts gift bags of toys together to sell at the flea market. She puts exactly 6 toys in each bag . She only sells full bags of toys. How many full bags of toys can she sell
Final answer:
Leah can make 46 full bags of toy cars to sell at the flea market when placing 6 toys in each bag out of her 280 toy cars, with 4 toys remaining unsold.
Explanation:
Leah has 280 toy cars and wants to sell them in gift bags, with 6 toys in each bag. To find out how many full bags she can sell, we need to divide the total number of toy cars by the number of toys per bag.
The calculation would be 280 ÷ 6 = 46 R4. This means Leah can make 46 full bags of toys and there will be 4 toys left over. Since she only sells full bags, the 4 extra toys will not be sold.
The science club is inflating a model of a hot air balloon. The graph below shows their progress. At what rate is the diameter increasing?
Answer:
12.5 centimeters per minute
Step-by-step explanation:
From the graph, the rate at which the diameter increasing would be inthe units of cm/min
The rate is basically the slope of the line. The slope (m) has formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex](x_1,y_1)[/tex] is any point from the graph
and
[tex](x_2,y_2)[/tex] is another point from the graph
Let's take the origin (0,0) as the first point and (4,50) as the second point. Now lets calculate the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{50-0}{4-0}\\m=\frac{50}{4}\\m=12.5[/tex]
Thus, we can say:
The diameter of the hot air balloon is increasing at a rate of 12.5 centimeters per minute
On a coordinate grid, AB has an end point B at (24, 16). The midpoint of AB is P(4, -3). What is the y-coordinate of Point A?
The y-coordinate of point A is -22
Step-by-step explanation:
Given
B = (24,16)
P = (4,-3)
The formula for mid-point of AB will be given by:
[tex]P = (\frac{x_A+x_B}{2} , \frac{y_A+y_B}{2})[/tex]
As we already know the y-coordinate of midpoint
We can put the formula's y coordinate equal to the given value
[tex]\frac{y_A+y_B}{2} = -3\\\frac{y_A + 16}{2 } = -3\\y_A+16 = -3 * 2\\y_A +16 = -6\\y_A = -6-16\\y_A = -22[/tex]
Hence,
The y-coordinate of point A is -22
Keywords: Mid-point, coordinate geometry
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The measure of the supplement of an angle is 12° less than twice the measure of the angle. What is the measurement, in degrees, of the angle and its supplement?
The measurement of the angle is ______ degrees.
The measurement of the supplement is ______ degrees.
Answer:
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
Step-by-step explanation:
Let the measure of the angle be 'x'.
Given:
Supplement of the angle is 12 less than twice the measure of the angle.
Twice the angle means 2 times of the angle which is [tex]2x[/tex] and 12 less means 12 is subtracted from [tex]2x[/tex].
So, supplement of the angle = [tex]2x-12[/tex]
Now, by definition of supplementary angles, if two angles are supplement of one another, then their sum is 180 degrees.
Therefore, the sum of the given angles = 180°
⇒ [tex]x+2x-12=180[/tex]
⇒ [tex]3x-12=180[/tex]
⇒ [tex]3x=180+12[/tex]
⇒ [tex]3x=192[/tex]
⇒ [tex]x=\frac{192}{3}=64\°[/tex]
The measure of the supplement = [tex]2(64)-12=128-12=116[/tex]
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
3,495 rounded to the nearest thousands
Answer:
The answer is 3000.
Step-by-step explanation:
Start to count from ones->tens->hundreds->thousands (from right to left). When it says nearest thousands, you should look at the previous no. which is in hundreds place. As the no. at hundreds place is lesser than 5, there's nothing to add up. (If no. is greater than 5, you should add 1 to the thousands place)
What is the domain and range of the relation shown in
the table?
Y
5
9
-1
5
X
10
15
19
32
A. domain: {−1, 5, 9}{−1, 5, 9} range: {10, 15, 19, 32}{10, 15, 19, 32}
B. domain: {10, 15, 19, 32}{10, 15, 19, 32} range: {−1, 5, 9}{−1, 5, 9}
C. domain: {10, 15, 19, 32}{10, 15, 19, 32} range: {y|y∈R}{y|y∈ℝ}
D. domain: {x|x∈R}{x|x∈ℝ} range: {−1, 5, 9}
Answer:
Domain : {10, 15, 19, 32}
Range: {-1, 5, 9}
Step-by-step explanation:
As the table of the relation is given as follows:
X Y
10 5
15 9
19 -1
32 5
From this table, we can define the relation by combining the ordered pairs from the table. Each and every order pair consists of x-coordinate and corresponding y-coordinate of any corresponding point.
So, the relation from the table can be made as follows:
relation : {(10, 5), (15, 9), (19, -1), (32, 5)}
Domain of a relation consists of all the x-coordinates (first elements) of order pairs.
Range of a relation consists of all the y-coordinates (second elements) of ordered pairs.
So, domain and range of relation will be as follows:
Domain : {10, 15, 19, 32}
Range: {-1, 5, 9}
Note: If there is any duplicate element in any x or y-coordinate of any ordered pair, it will be written only once when we determine domain and range. Here, in this example, 5 is duplicate, so, it will be mentioned only one time when we determine the range of this relation.
Keywords: domain, relation, range
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The domain and range of the relation given in the table are the sets of x-values and y-values respectively. In this case, the domain is {-1, 5, 9} and the range is {10, 15, 19, 32}, which corresponds to Option A.
To determine the domain and range of the relation shown in a table, we must look at the set of ordered pairs provided. The domain consists of all the first elements in these pairs, which represent the x-values, while the range consists of all the second elements, which are the y-values. Looking at the table, we can list the x and y values separately to clearly identify the domain and range.
If the table of the relation presents the ordered pairs as (X, Y), interpreting the question that the domain should be {-1, 5, 9} and the range should be {10, 15, 19, 32}, then the correct option would be:
Option A.
Domain: \{-1, 5, 9\} and Range: \{10, 15, 19, 32\}.
It is essential to note that a function is a special relation where each element of the domain maps to a unique element in the range. In this case, as each x-value maps to a distinct y-value, it suggests the relation is indeed a function.
20% of a number is 35 what is the number
Solve for x.
20% × x = 35
0.2x=35
x=175
answer: 175
Answer: 175
Step-by-step explanation: We can change this problem to mean the same thing but it will say 20% of what number is 35.
To answer the question 20% of what number is 35, we translate the question into an equation. First we have 20% which we need to write as a decimal and remember to write 20% as a decimal, we move the decimal point 2 places to the left and we get 0.20.
Next we have "of what number" that's times x, "is 35" = 35. Now we have the equation (.20)(x) = 35.
Not to solve for x, since x is being multiplied by .20, we need to divide by .20 on both sides of the equation. On the left side of the equation the .20's cancel and we have x. On the right side of the equation we have 35 divided by .20 which is 175.
This means that 20% of 175 is 35.
Julian saves 5/7 of the money he makes babysitting. What is 5/7 written as a decimal ?
Answer:
0.714
Step-by-step explanation:
Answer:
0.714...
Step-by-step explanation:
5/7 means 5 divided by 7=
0.71428571...= 0.714(rounded)
How do you solve 3/4x=-24
Answer:
x = -32
Step-by-step explanation:
¾ x = -24
Multiply both sides by 4.
3x = -96
Divide both sides by 3.
x = -32
Answer:
x = -2
Step-by-step explanation:
Divide -24 by 3 = -8
4x=-8
Divide -8 by 4 = -2
x = -2
Part II: Convert 7.75 pounds to ounces.
A. Create a conversion ratio that relates pounds to ounces (2 points)
B. Multiply the given number of pounds by the conversion ratio you found in A. Show your work
(2 points)
Answer:
Step-by-step explanation:
A. The conversion ratio is that 16 oz = 1 lb
B. 7.75 lb × [tex]\frac{16oz}{1lb}[/tex]
From there the label of lb cancels out, leaving you with the label oz. Multiply straight across the top to get 124 oz.
PLZ HELP I BEG YOU ITS URGENT
James deposited $575 into a bank account that earned 5.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 2 1/2 years? Round your answer to the nearest cent.
Answer:
$638.25
Step-by-step explanation:
The interest is 5.5% yearly and it is simple interest.
Now, if we consider a deposit of $575 into the bank account that earned 5.5% simple interest each year, then after 2 and half years James will get interest only for 2 years as the 3rd year's interest will be added after the 3rd year.
Therefore, if no money was deposited into or withdrawn from the account, then after 2.5 years the sum will be
[tex]575(1 + \frac{5.5 \times 2}{100}) = 638.25[/tex] dollars. (Answer)
Using the expressions above, find the cost to the family of each company's phone plan if:
a. Four people want a phone line, four people want unlimited texting, and the family needs two interna
Company A
Company B
Company C
Which cell phone company should John's family use? Why?
Answer:
company B
Step-by-step explanation:
the company is good!
Final answer:
To find the cost to the family of each company's phone plan, we calculated the total cost for four phone lines and four unlimited texting plans, as well as the cost for two international calls. Based on the calculations, John's family should use Company A because it has the lowest total cost of $100.50.
Explanation:
To find the cost to the family of each company's phone plan, we need to calculate the total cost for four phone lines and four unlimited texting plans, as well as the cost for two international calls. Let's calculate the cost for each company:
Company A:
Cost for four phone lines = 4 * $20 = $80
Cost for four unlimited texting plans = 4 * $5 = $20
Cost for two international calls = 2 * $0.25 = $0.50
Total cost for the family with Company A = $80 + $20 + $0.50 = $100.50
Company B:
Cost for four phone lines = 4 * $15 = $60
Cost for four unlimited texting plans = 4 * $10 = $40
Cost for two international calls = 2 * $0.50 = $1
Total cost for the family with Company B = $60 + $40 + $1 = $101
Company C:
Cost for four phone lines = 4 * $25 = $100
Cost for four unlimited texting plans = 4 * $8 = $32
Cost for two international calls = 2 * $0.15 = $0.30
Total cost for the family with Company C = $100 + $32 + $0.30 = $132.30
Therefore, John's family should use Company A because it has the lowest total cost of $100.50.
How do you get 7.5/8
Answer:
0.9375
Step-by-step explanation:
Do the long division and you'll find the answer.
A triangular banner has an area of 5ft squared. The height is 3 ft more than the base. Find the base and the
height.
Answer: base a=2ft
height hₐ=5ft
Step-by-step explanation:
use equation for area of triengle
A=a*hₐ/2
hₐ-height of tringle
a-base of triangle
hₐ=a+3
A=a(a+3)/2
2A=a²+3a
A=5ft
2*5=a²+3a
a²+3a-10=0
a=(-3±√9+40)/2
a=(-3±7)/2
a=-5ft
a=2 ft
hₐ=2+3=5ft
0.00035 + (4.2 x 10-5)
Step-by-step explanation:
Solve the bracket first. starting with multiplication and then subtraction
0.00035 + (4.2 x 10-5)
0.00035 + (42-5)
0.00035 + 37
0.01295
Write the number 110 as a sum of hundred and tens
Answer:
100+10
Step-by-step explanation:
A soccer game is 90 minutes long. 36 minutes have passed. What percentage of the game has passed?
Answer:
40%
Step-by-step explanation:
Percentage Passed = 36 ÷ 90 × 100 = 40%
does anyone know to do this
All the information is in the problem you just have to format it into an equation.
Point slope form: [tex]y_{2}-y_{2}=m(x_{2}-x_{1})[/tex] where "m" is the slope.
The equation would look like...
y+6=[tex]\frac{1}{5}[/tex](x+4)
Find the value of X please!!!
Answer:
What are we finding for X?
Step-by-step explanation:
Because the polygons are similar... we can create this proportion relationship.
[tex]\frac{8}{10} = \frac{4}{x}[/tex]
Using cross multiplication...
4·10=8x
8x=40
x=5
answer: x=5
HELP I WILL GIVE BRAINLIEST THANKYOU PLEASE YOU DONT HAVE TO ANSEER ALL
Answer:
none of the above
Step-by-step explanation:
PLEASE MARK BRAINLIEST!
Answer:
Sorry for the incorrect answer everyone!
Step-by-step explanation:
My old answer: Perpendicular bisector
THE CORRECT ANSWER: None of the aboveReasons:
Median doesn't relate to this problemAltitude doesn't relate to this problemA perpendicular bisector cuts through a line segment, making an angle of 90. This triangle does not show thatThe answer is none of the above, because none of the other answers make sense.I know I made a mistake before, but this is better late than never! I hope this helps for the future! *^-^*
- sincerelynini
-x+8=6 what is the answer for x
Answer:
x=-2
Step-by-step explanation:
-2+8=6
subtract 8 from six and you get your answer since it is a simpler linear equation. hoped this helped a little bit
Answer:2
Step-by-step explanation:
-X+8=6
a dozen apples cost$4.92 for a dozen apples is a ratio of what per Apple
Final answer:
Each apple costs 41 cents when a dozen apples are bought for $4.92, determined by dividing the total cost by the number of apples.
Explanation:
The question asks to find the cost per apple when a dozen apples are purchased for $4.92. To find the cost per individual apple, you divide the total cost by the number of apples. There are 12 apples in a dozen, so:
$4.92 ÷ 12 apples = $0.41 per apple
So, each apple costs 41 cents. This exercise of finding the individual cost from a total is an example of a ratio used in basic arithmetic, often taught in middle school mathematics.
Robin can clean
72
7272 rooms in
6
66 days.
How many rooms can Robin clean in
9
99 days?
Robin can clean 108 rooms in 9 days, given she cleans 72 rooms in 6 days; this is determined by calculating her daily cleaning rate and extending it over the 9-day period.
The student asks how many rooms Robin can clean in 9 days if she can clean 72 rooms in 6 days. To solve this problem, we first need to determine the rate at which Robin cleans rooms per day, which is done by dividing the total number of rooms by the total number of days. Once we have the daily rate, we can then multiply this rate by 9 to find out how many rooms can be cleaned in 9 days.
First, we calculate the daily rate:
Rate = Total Rooms / Total Days
Rate = 72 rooms / 6 days
Rate = 12 rooms/day.
Now, we multiply the daily rate by 9 days:
Rooms in 9 days = Rate times Number of Days
Rooms in 9 days = 12 rooms/day times 9 days
Rooms in 9 days = 108 rooms.
Therefore, Robin can clean 108 rooms in 9 days.
Lexi has $80 to spend on an ice cream treat each week. If she spends $4 on ice cream per week, the function C(x)=80−4x
C
(
x
)
=
80
-
4
x
represents how much ice cream money, C, Lexi has left after a certain number of weeks, x. What is the domain in the context of the problem? Why?
Answer:
Domain[tex]=\{1,2,3,4,5,6,7,8,9,10,11,12,,13,14,15,16,17,18,19,20\}[/tex]
In other words Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]
Step-by-step explanation:
[tex]C(x)=80-4x[/tex]
Let after [tex]t[/tex] weeks she has left no money.
[tex]c(t)=0\\80-4t=0\\4t=80\\t=20[/tex]
That means she can have money for ice cream from the week 1 to week 20 and after that she will have no money.
So [tex]x[/tex] can be any number between [tex]1[/tex] and [tex]20[/tex]
Hence Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]