Step-by-step explanation:
5,555 can be rounded up to 6,000 because the 5 next to the five thousand will make it go up. while the 4,444 will round to 4,000 . I don't have a clear answer but I hope this helps.
Solve by completing the square
[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]
Please I need your help
find the area of a circle that has the diameter of 2 feet. ( use 3.14 for pi)
Answer: area of the circle is [tex]3.14ft^{2}[/tex]
Step-by-step explanation:
1. the equation to find the area of a circle is [tex]\pi r^{2}[/tex]
2. the diameter is equal to 2r, meaning to get the radius, divide the diameter by 2. [tex]\frac{2}{2} =1[/tex]
3. plug in the the radius into the equation. [tex]3.14*1^{2} =3.14ft^{2}[/tex]
hope this helped! ♡
What is the area of the parallelogram QRST?
[tex]\text{Area of parallelogram QRST} = QR \times TU = 20 ~in \times 18~in =360 in^2[/tex]
What is the value of e?
1190
c
a
O A. 22°
OB. 48°
0 C. 61°
O D. 180°
Answer:
C. 61 degrees
Step-by-step explanation:
a line is 180 degrees
so e and 119 degrees makes a line
so you subtract 180-119= 61 degrees
write an equation for the graph below in the terms of x
The number 2 in the expression 5 + 2x is called the
coefficient of x. How does changing the coefficient to
6 change the meaning of the expression?
Changing the coefficient of x to 6 changes the meaning of the expression as 5 is added to 6 times x
Solution:
Given that number 2 in the expression 5 + 2x is called the coefficient of x
We are asked to find what happens when changing the coefficient to 6 changes the meaning of the expression
In the expression,
5 + 2x
This means 5 is added to 2 times x or 5 is added to twice of x
Number 2 is called the coefficient of x
When we change this coefficient to 6, the expression becomes,
5 + 6x
So now the meaning of expression becomes,
5 is added to 6 times x
So changing the coefficient of x changes the meaning of the expression
You spent $24 more than Pam. If you spent $82, how much money did Pam spend?Write and solve an equation.
Answer:
58
Step-by-step explanation:
its basically saying that pam spent 24 dollars less than you. soo 82 - 24 = 58
*Pls help me*
No links
Answer:
See below ↓
Step-by-step explanation:
a. 4 ÷ (2/3) = 12/3 ÷ 2/3 = 12 ÷ 2 = 6
b. 4 ÷ 1 = 4
Attachment below.
Answer:
1: 6
2:4
Step-by-step explanation:
Rocio drops a ball from a height of 4 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, as shown at left. Which of the following equations correctly models the ball's peak height, h, in meters, after b bounces?
The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:
[tex]H(b) = 4(0.79)^b[/tex]
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
Rocio drops a ball from a height of 4 meters, hence A(0) = 4.Each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, hence 1 - r = 0.79.Thus, the equation is given by:
[tex]H(b) = 4(0.79)^b[/tex]
More can be learned about exponential equations at https://brainly.com/question/25537936
100 divided by 35,513.22
Answer:
0.002816 or 0.003
Step-by-step explanation:
Be sure to use a calculator to double check the answer
Hope this helps!
sophia has 8 spend on lunch .Does she have enough money for a sandwich a drink and a bag of chips
Answer:
depends on how much each thing costs
Step-by-step explanation:
After a 25% reduction, a sweater is on sale for $41.25.
What was the original price?
Let the original price be x.
x * (1 - 0.25) = $41.25
0.75x = $41.25
x = $41.25 / 0.75 = $55
Answer:
$55
Step-by-step explanation:
____ decrease by 25%= $41.25, which the unknown number is $55.
Write the equation of the trigonometric graphs.
Answer:
[tex]2 \cos(4x) [/tex]
Step-by-step explanation:
The highest and lowest value is 2 and -2 respectively so the amplitude is 2.
That also means the vertical translation is 0.
The graph is reaches it max every pi/2 units so the period is
pi/2.
Since the graph intersects a non zero value at 0, it will be the cosine function.
Step 2: A cosine function is
[tex]a \cos(b(x - c)) + d[/tex]
where a is the amplitude
[tex] \frac{2\pi}{ |b| } [/tex]
is the period
C is the horinzontal shift
d is the vertical shift
We know a is 2
D is 0.
To find b,
[tex] \frac{2\pi}{b} = \frac{\pi}{2} [/tex]
[tex]b = 4[/tex]
So as of right now we have
[tex]2 \cos(4x) [/tex]
Answer(s):
[tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}) \\ y = 2cos\:4x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:4x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [\frac{5}{8}\pi, 0],[/tex]from there to [tex]\displaystyle [\frac{\pi}{8}, 0],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
If $2,000 is invested at 4% annual interest compounded quarterly, how long would it take for the account balance to reach $10,000? Round your answer to the nearest tenth.
Answer:
40.2 years
Step-by-step explanation:
Use the compound amount formula A = P(1 + r/n)^(nt), in which n represents the number of compounding periods per year. In this case n = 4. Solve the following equation for t (years):
$10,000 = $2,000(1 + 0.04/4)^(4t):
This is equivalent to
5 = 1.01^(4t). Taking the natural logarithm of both sides, we get:
ln 5 = 4t·㏑ 1.01, or
ln 5 1.609
-------------- = t = -------------- = 40.2 years
4·ln 1.01 4(0.010)
Write the equation of the exponential function, base 2.
Answer:
y=4(12)x
Step-by-step explanation:
An exponential function is in the general form
y=a(b)
18. Find the present value of a deferred annuity of ₱ 30,000.00 at the end of every year for 10 years. The first payment of a mother will be done at the end of the second year, and the money is compounded at 3% annually. a. ₱ 244,354.12 b. ₱ 248,452.51 c. ₱ 278,520.14 d. ₱ 291,245.18
Answer:
₱ 248,452.51
Step-by-step explanation:
₱ 248,452.51
Answer: people in the US will spend____ billion dollars on statins in 2016
Answer:
38.5
Step-by-step explanation:
The equation says
S - 1.8x = 6.1, where x is the amount of years after 1998.
2016 is 18 years after 1998.
S - 1.8*18 = 6.1
S= 32.4 + 6.1
S= 38.5
A bead is formed by drilling a cylindrical hole of 2mm diameter through a sphere with an 8mm diameter. Estimate the volume of the bead to the nearest whole?
Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.
What is the Volume of a Sphere and a Cylinder?Volume of a sphere = 4/3πr³Volume of a cylinder = πr²hVolume of the bead = Volume of the sphere - volume of the cylindrical hole
= 4/3π(4³) - π(1²)(8)
= 268.08 - 25.13
Volume of the bead = 242.95 mm³
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I NEEDDD HELPPPP 50PTS !!!!!!!!!!!!!!
Answer:
$1225
$33,775
Step-by-step explanation:
Given:
price of current model = $35,000next model = 3.5% LESS than price of current modelTo find a percentage of an amount, convert the percentage into a decimal and multiply it by the amount:
3.5% = 3.5/100 = 0.035
⇒ Decrease in price = 0.035 × 35000 = $1225
Price of next model = price of current model - decrease in price
= 35000 - 1225
= $33,775
Decrease amount:-
3.5% of 350000.035(35000)$1225So
New price:-
35000-1225$33775d If the width of a rectangle with perimeter P is 6 units, what is its length?
Step-by-step explanation:
width is 6 units
P=2(l+w)
p=2(l+6)
l+6=p/2
l= (p/2)-6
The length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.
What is the perimeter of a rectangle?A perimeter is a closed route that surrounds, outlines, or embraces a rectangle. The perimeter of a rectangle is given by the formula,
[tex]\rm Perimeter= 2(Length +width)[/tex]
As it is given that the width of the rectangle is 6 units, while the perimeter of the rectangle is P. Now if we write about the perimeter of the rectangle, it can be written as,
[tex]\rm Perimeter= 2(Length +width)[/tex]
[tex]P = 2(l+6)\\\\\dfrac{P}{2} = (l+6)\\\\l = \dfrac{P}{2}-6[/tex]
Hence, the length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.
Learn more about Perimeter:
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Stuart and Francisco designed a black rocket and a white rocket during an aerospace class. Both rockets were launched after class. During the launch, Stuart and Francisco recorded data of their rockets trajectories. Stuart modeled the black rockets distance from the ground, in feet, x seconds after it was launched with the graph. Francisco modeled the white rockets distance from the ground, in feet, x seconds after it was launched with the function g(x)= -16x^2 + 50x +7 . Both wanted to know what the greatest distance was from the ground for each rocket. Stuart obtained that his rockets greatest distance from the ground was [Drop down 1] while Francisco obtained a greatest distance of [Drop down 2].
We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft
How to get the greatest distance from the ground?In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.
In the case of Francisco, we need to find the maximum of:
g(x)= -16x^2 + 50x +7
Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.
x = -50/(2*-16) = 25/16
Evaluating the function in 25/16 we get:
g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft
If you want to learn more about quadratic functions, you can read:
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please someone help me! I’m not accepting any links or files.
:)
Answer:
400
Step-by-step explanation:
48 is 12% of x
12/100 = 48/x
3/25 = 48/x
1/25 = 16/x
x = 25 × 16
x = 400
Answer: 400
Answer:
400
Step-by-step explanation:
(48 x 100) / 12 = 400
100 POINTS!!!!!!!
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?
Part B: What are the exact values of all six trigonometric functions evaluated at θ?
Answer:
A. coterminal angle = 4π/3
B. sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;
sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3
Step-by-step explanation:
A.Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle
coterminal angle = -8π/3 +4π = -8π/3 +12π/3
coterminal angle = 4π/3
__
B.The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.
sin(θ) = -√3/2 . . . csc(θ) = -2√3/3
cos(θ) = -1/2 . . . sec(θ) = -2
tan(θ) = √3 . . . cot(θ) = √3/3
Work out the length of X.
25 cm
х
24 cm
The diagram is not drawn accurately.
0
cm
Answer:
By Pythagoras theorem
H^2=P^2+B^2
25^2=x^2+24^2
625=x^2 + 576
625-576=x^2
49=x^2
x^2=49
x=√49
x=7cm
Hope this helps uhh
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
The probability of getting at least 1 blue is 6/11
Let me know if you want an explanation :)
Paul rents a car for $30 a day. Write an expression to show the relationship between the number of days Paul rents the car and the total dollars (t) he spends?
The expression that can be used to show the relationship between the number of days and the total dollars (t) he spends is t = 30d
How to write expressionsCost of renting a car per day = $30Number of days Paul rents the car = dTotal amount John spends = $tThe equation:
Total = cost per day × number of days
t = 30 × d
t = 30d
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The diagram shown is two intersecting lines. The measure of 5 is 47°.
Answer:
a) 37º
b) 143º
c) 2x - 5 = 143
Step-by-step explanation:
a) Angles 5 and 7 are vertical angles and therefore have the same measurements.
b) Angles 5 and 6 form a straight line and are therefore supplementary (add up to 180º). 180 - 37 = 143.
c) We found the measure of angle 6 is 143º in part b. We can set that equal to 2x - 5. Therefore the equation is 2x - 5 = 143.
Shania is making eight gift bags to give out to her friends coming over to her house for a movie night. Each gilt bag will con
polishes and a manicure kit. Including tax, each nail polish costs $2.50 and each manicure kit costs $4.00.
The following expression shows the amount of money Shania will spend on gift bags.
8(2.5x + 4)
Answer: 20x + 32 or $20 spent on the nail polish & $32 spent on the kits
Formula:
bags($polishx + $kit)
Work:
8(2.5x + 4)
8 x 2.5x = 20x
8 x 4 = 32
which of the points shown below given by the equation y=x
Answer:
I believe its D
Step-by-step explanation: X and Y are both -3