sin(x) = 1/2 when x is 30°, 150°, 210°, or 330° (unit circle).
With those angles, the cos(x) is ±√3/2 and the tan(x) is ±√3/3.
Answer:
[tex]cos(x)=\pm \frac{\sqrt3}{2}[/tex]
[tex]\tan(x)= \pm \frac{1}{\sqrt3}[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]\sin(x) = \displaystyle\frac{1}{2}[/tex]
We use the trigonometry identity:
[tex]\sin^2(x) + cos^2(x) =1[/tex]
Putting the value, we get,
[tex]\bigg(\displaystyle\frac{1}{2}\bigg)^2 + \cos^2(x) = 1\\\\\cos^2(x) = \frac{3}{4}\\\\\cos(x)=\pm \frac{\sqrt3}{2}[/tex]
Formula:
[tex]\tan(x) = \displaystyle\frac{sin(x)}{cox(x)}\\\\tan(x) = \frac{\pm \frac{1}{2}}{\frac{\sqrt3}{2}} = \pm \frac{1}{\sqrt3}[/tex]
what is the correct first step to solve this system of equations. 4x-3y=-10, 2x+3y=4
a) add the 2 equations together
b) subtract the 2 equations
c) multiply the second equation by 3
D) divide the first equation by 4
Answer:
best bet is c
The correct first step is : " add the 2 equations together "
What is Equation?
An equation is a mathematical statement with an '=' symbol between two expressions that have equal values.
Here, given equations are
4x - 3y = -10
2x + 3y = 4
In given equation the coefficient of y is equal with opposite sign, so for simplification of these equation we need to add these equation.
Thus, the correct first step is : " add the 2 equations together "
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A parallelogram-shaped tile has an area if 48 in.2. The base of the tile measures 12in. What is the measure of bits height
Answer:
height = 4 in
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = base × height ← substitute values
48 = 12 × height ( divide both sides by 12 )
4 = height
On a coordinate plane, what is the distance between the points (-4, -3) and (-1, 5)? Round your answer to the nearest hundredth.
Answer:
8.54
Step-by-step explanation:
To find the distance between 2 points
d = sqrt( y2-y1)^2 + (x2-x1)^2)
where (x1,y1) and (x2,y2) are the two points
d = sqrt((5--3)^2+ (-1--4)^2)
= sqrt((5+3)^2+ (-1+4)^2)
= sqrt((8)^2+ (3)^2)
= sqrt(64+ 9)
=sqrt (73)
=8.544003745
Rounding to the nearest hundredth
=8.54
ANSWER
The distance between the two points is 8.54 to the nearest hundredth.
EXPLANATION
We want to find the distance between the the points (-4, -3) and (-1, 5).
We use the distance formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{( - 1 - -4)^2+(5- - 3)^2}[/tex]
[tex]d=\sqrt{( 3)^2+(8)^2}[/tex]
[tex]d=\sqrt{9+64}[/tex]
[tex]d = \sqrt{73} [/tex]
[tex]d = 8.544[/tex]
To the nearest hundredth the distance is 8.54 units.
A child’s toy harp is in the shape of a trapezoid as shown.
In square inches, what is the area of the harp?
Hello! your answer is going to be 64 square inches.
The equation to get this is as listed:
[tex]Area = \frac{Base1+Base 2}{2} * Height[/tex]
I hope this helps, and have a nice day!
Answer:
a = 64 ft²
Step-by-step explanation:
a = a + b (h)
2
a = 4 + 12/2 (8)
a = 16/2 (8)
a = 8 (8)
a = 64 ft²
An element with mass 570 grams decays by 26.9% per minute. How much of the element is remaining after 14 minutes, to the nearest 10th of a gram?
Answer:
7.1
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }570
a=starting value = 570
r=\text{rate = }26.9\% = 0.269
r=rate = 26.9%=0.269
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.269=0.731
b=1−r=1−0.269=0.731
\text{Write Exponential Function:}
Write Exponential Function:
y=570(0.731)^x
y=570(0.731)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=570(0.731)^{14}
y=570(0.731)
14
y= 7.091174
y=7.091174
Evaluate
y\approx 7.1
y≈7.1
round
To calculate the remaining amount of an element undergoing exponential decay, use the formula A = A0 * (1 - r)^t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute, and t is the time in minutes. In this case, approximately 12.3 grams of the element is remaining after 14 minutes.
Explanation:
To calculate the amount of the element remaining after 14 minutes, we need to use the formula for exponential decay, which is A = A0 * (1 - r)t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute (in decimal form), and t is the time in minutes.
In this case, the initial amount is 570 grams, the decay rate is 26.9% or 0.269 per minute, and the time is 14 minutes.
Plugging these values into the formula, we get:
A = 570 * (1 - 0.269)14 = 570 * (0.731)14 = 570 * 0.0221 = 12.27 grams.
Therefore, approximately 12.3 grams of the element is remaining after 14 minutes.
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Who reads at the same rate?
Answer:
Alexis and Jon reads at the same rate, 0.67 page by min
Step-by-step explanation:
Rate Alexis = 30/45 pages/min = 0.67 page by min
Rate Jon = 40/60 pages/min = 0.67 page by min
Rate Sal = 45/90 = 0.5 page by min
Rate Andre = 15/25 = 0.6 page by min
Then
Alexis and Jon reads at the same rate, 0.67 page by min
Best regards
How do you solve -3x-4>5
Answer:
x<−3
Step-by-step explanation:
−3x−4>5
Step 1: Add 4 to both sides.
−3x−4+4>5+4
−3x>9
Step 2: Divide both sides by -3.
−3x
−3
>
9
−3
x<−3
Answer:
x < -3
Step-by-step explanation:
We must isolate x.
Start by adding 4 to both sides, obtaining -3x > 9.
Next, divide both sides by -3, remembering to reverse the direction of the > symbol:
-3x 9
------ > ----- ↔ x < 9/(-3), or x < -3
-3 -3
A used motorcycle is on sale for $3,600. Erik makes an offer equal to 3/4 of this price. How much does Erik offer for the motorcycle?
2,700 I'm pretty sure.
Z varies inversely with x and directly with y. When x=6 and y=2 z=5 what is the value of a when x=4 and y=9
Answer:
15·9
z = --------- = 135/4
4
Step-by-step explanation:
The general formula here is as follows:
ky
z = ---------
x
We must find the value of the constant of proportionality. To do this, subst. 6 for x, 2 for y and 5 for z and compute k:
k·2
5 = ---------
6
Multiplying both sides by 6 results in 30 = 2k.
Thus, k = 30/2, or k = 15.
Our formula becomes:
15y
z = ---------
x
if x = 4 and y = 9, we get:
15·9
z = --------- = 135/4
4
Answer:
[tex]z=33.75[/tex]
Step-by-step explanation:
We are given that z varies inversely with x and directly with y when x=6 and y=2 then z=5
We have to find the value of z when x=4 and y=9
According to question
[tex]z\propto\frac{1}{x}[/tex]
and [tex]z\proptoy[/tex]
Therefore, we have [tex]z\propto\frac{y}{x}[/tex]
[tex]z=k\frac{y}{x}[/tex]
k=proportionality constant
Substitute x=6 , y=2 and z=5 then we get
[tex]5=k\times \frac{2}{6}[/tex]
[tex]5=\frac{k}{3}[/tex]
[tex]k=5\times3[/tex]
By division poperty of equality
k=15
Now, substitute the value x=4,y=9 and k=15 then the value of z
[tex]z=15\times \frac{9}{4}[/tex]
[tex]z=\frac{135}{4}[/tex]
[tex]z==33.75[/tex]
You plan to invest $350 $350 in a growth fund that has a rate of 1.5% 1.5% compounded quarterly. How much money will this investment be worth after 50 50 years? Round to the nearest cent.
Is this a scatterproblem?
If so then 350×((1.5)^4)^50 would be an answer?
Answer:
the answer is 739.91
Step-by-step explanation:
i put this problem for my question and got it right on the test.
good luck!
Which two wholes numbers does 3 2/10 lie between?
Answer:
3 and 4
Step-by-step explanation:
On a number line, 3 2/10 is greater than 3, by 1/5, but less than 4, by 4/5.
3 and 4 are two whole numbers that come after each other.
Answer:
3 and 4
Step-by-step explanation:
3 2/10 is in-between the numbers 3 and 4
convert 18/5 to a decimal using long division
Answer:
3.60
Step-by-step explanation
you need to turn it to 100 then move the decimal 2 places to the left
Answer:
A. 3.6
Step-by-step explanation:
Please help we with all
Step-by-step explanation:
[tex]1)\ \dfrac{10}{100}=0.10=0.1\\\\2)\ \dfrac{5}{10}=0.5\\\\3)\ \dfrac{6}{10}=0.6\\\\4)\ \dfrac{93}{100}=0.93\\\\5)\ \dfrac{1}{10}=0.1\\\\6)\ \dfrac{40}{100}=0.40=0.4\\\\7)\ \dfrac{56}{100}=0.56\\\\8)\ \dfrac{7}{10}=0.7\\\\9)\ \dfrac{3}{10}=0.3\\\\10)\ \dfrac{98}{100}=0.98\\\\11)\ \dfrac{4}{10}=0.4\\\\12)\ \dfrac{78}{100}=0.78[/tex]
What is an IQR? Help Please!
Answer:
in math it should be Interquartile Range
Step-by-step explanation:
Answer:
Interquartile range
Step-by-step explanation:
In descriptive statistics, the interquartile range, also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q₃ − Q₁.
the expression below is a factorization of which of the following trinomials (3x-4)(x-1)
3x^2 - 7x + 4
Hope this is the answer you're searching for
Use the quadratic model y=-4x^2-3x+4 to predict y if x equals 5.
Answer:
y = - 111
Step-by-step explanation:
Substitute x = 5 into the quadratic for y
y = - 4(5)² - 3(5) + 4 = - 100 - 15 + 4 = - 111
Ben says 7 9/100 must be less than 7. 2/10 because 9 hundredths is less than 2 tenths. Do you agree? Draw a line to support your answer
Yes, I cannot draw a line because this is online. Sorry
The growth of a new strain of bacteria is represented by y=79.31(1,48)^x,where x represents the number of days a y represents the number of bacteria.which is the best prediction for the number of bacteria on day 6
Answer:
Choice D; 833
Step-by-step explanation:
The best prediction for the number of bacteria on day 6 will be given by substituting x with 6 in the exponential growth model;
[tex]y=79.31(1.48)^{x}\\y=79.31(1.48)^{6}\\y=833[/tex]
What is the solution to the following system of equations?
Answer:
(3,2)
Step-by-step explanation:
Make sure you use substitution to solve the equation for either x or y first. Then once you have the value of one, plug it into the equation to solve for the value of the other.
The answer is the third one.
you bought a video game for 50$,but it loses 25% of its value every six months. how much will the video game be worth after two years
keeping in mind that two years is 24 months, and we know that cyclically it's losing 25% every 6 months.
[tex]\bf \textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &24\\ c=period\dotfill &6 \end{cases} \\\\\\ A=50(1 - 0.25)^{\frac{24}{6}}\implies A=50(0.75)^4\implies A\approx 15.82[/tex]
If f(x) = x+4 and g(x) =x^3, what is (g•f)(-3)
ANSWER
[tex](g\circ f)( - 3) = 1[/tex]
EXPLANATION
The given functions are
[tex]f(x) = x + 4[/tex]
and
[tex]g(x) = {x}^{3} [/tex]
The composite function,
[tex](g\circ f)(x) = g(f(x))[/tex]
[tex](g\circ f)(x) = g(x + 4)[/tex]
[tex](g\circ f)(x) = ( {x + 4)}^{3} [/tex]
We now substitute x=-3 to obtain:
[tex](g\circ f)( - 3) = ( { - 3 + 4)}^{3} [/tex]
[tex](g\circ f)( - 3) = ( {1)}^{3} = 1[/tex]
Answer:
The answer is 1
What is the surface area of the regular pyramid?
You would have to do 18x2 then 14x2.
Answer:
Step-by-step explanation:
Surface area = [tex]lw+l\sqrt{(\frac{w}{2})^2+h^2}+w\sqrt{(\frac{l}{2})^2+h^2}[/tex]
just put the values in the formula h=18,w=14,l=14
A prism has the surface area of 100 cm². What sentence describes the effect of measuring the surface area in square millimeters?
A. The Surface area increases
B. The Surface area decreases
C. The surface area stays the same, but the number representing the surface area increases.
D. The surface area stays the same, but the number representing the surface area decreases.
Answer:
A. The surface area stays the same, but the number representing the surface area increases.
Answer:
C
Step-by-step explanation:
PLEASE HELP
Triangle FGH was dilated to create triangle ABC.
What is the scale factor of the dilation?
3
1/3
2
1/2
Answer:
1/2
Step-by-step explanation:
Triangle FGH was dilated to create triangle ABC
The image is a reduction so scale factor is between 0 and 1
2.5/5 = 3.5/7 = 4.3 / 8.6
= 0.5
= 1/2
Answer
1/2
The scale factor of the dilation is,
⇒ 1 / 2
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Triangle FGH was dilated to create triangle ABC.
Hence, For scale factor,
Since, Triangle FGH was dilated to create triangle ABC
So, We get;
The scale factor is,
2.5/5 = 3.5/7 = 4.3 / 8.6
2.5 / 5 = 1/2
3.5/7 = 1/2
4.3/8.6 = 1/2
Therefore, The scale factor of the dilation is,
⇒ 1 / 2
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find the mode for a data set. 18,24,24,24,25,37,37,46
Answer:
24 is the mode
Step-by-step explanation:
Mode is the number that is most often seen.
18 is seen 1 time
24 is seen 3 times
25 is seen 1 time
37 is seen 2 times
46 is seen 1 time
24 is the mode because it is seen the most often.
Answer:
24
Step-by-step explanation:
The mode is the number that appears the most times in a data set. Here, 24 occurs the most (3 times)
Emmanuel added 8 links per minute to his chain mail. Allesia started 20 minutes after Emmanuel and added 13 links per minute to her chain mail. How long had Emmanuel worked when Allesia caught up to him, and how many links had he added?
Answer: 52 minutes, 416 links
Step-by-step explanation:
8*20=160
13-8=5
160/5=32
32+20=52
52*8=416
Find the area of the polygon.
Answer:
2,400 cm²
Step-by-step explanation:
You can solve for x because you know that 40cm=x²+4cm:
36 cm = x²
x = 6cm.
Therefore the width is 2(6)²-12, which is 60cm.
So the area is 40 cm x 60 cm, which is 2,400 cm².
if n/5=45/75.find the value of n.
Start with
[tex]\dfrac{n}{5}=\dfrac{45}{75}[/tex]
Multiply both sides by 5:
[tex]n = \dfrac{45\cdot 5}{75} = \dfrac{45}{15} = 3[/tex]
Answer:
n = [tex]\frac{9}{5}[/tex]
Step-by-step explanation:
Simplify the fraction on the right side
[tex]\frac{n}{5}[/tex] = [tex]\frac{45}{75}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5n = 15 ( divide both sides by 5 )
n = 3
which equation describes the porportion: the number of chickens (c) is four times as many the number of horses (h) on the farm
Answer:
c4:h1
Step-by-step explanation:
Answer:
c=4h
Step-by-step explanation:
How old am i if 500 reduced by 3 times my age is 266
Hey there!
Let's start by making an equation to represent this.
500 - 3a = 266
Reduced by is the same as subtracting, and a represents age.
Subtract 500 from both sides.
-3a = -234
Divide each side by -3.
a = 78
Check.
500 - 3(78) = 266
500 - 234 = 266
266 = 266
You are 78 years old.
Hope this helps!
Answer: Age=78
Step-by-step explanation:
500-(3xAge)=266
500-266=3xAge
(500-266)/3 = Age