Answer:
x = 4√2
Step-by-step explanation:
x² - 33 = -1 [ change sides ]
x² = -1 + 33
x² = 32
x = √3 [changing sides, changes power of square, (²) turns square root,√ ]
x = √4 * 4 * 2
x = 4√2 .......final answer.
Answer:
x = 4√2 or x = −4√2
Step-by-step explanation:
Step 1: Add 33 to both sides.
x2 − 33 + 33 = −1 + 33
x2 = 32
Step 2: Take square root.
x = ±√32
x = 4√2 or x = −4√2
A bag contains 4 red marbles , 8 blue marbles and 5 green marbles . If three marbles are drawn out of the bag what is the probability to the nearest 1000th that all three marbles drawn will be green '
Pleaseee help this is compound probability..
Answer:
0.025
Step-by-step explanation:
The solution is in the attached file
Mrs. Hernandez earns $35.60 per hour and in one week earned $854.40. For how many hours did she work last week? What expression matches A: 8,544 divided by 356 B: 85,440 divided by 356 C. 8,560 divided by 544
Answer:
Option A
Step-by-step explanation:
Given the following question:
Mrs. Hernandez earns $35.60 an hour
One week she earned $854.40
To find the answer we divide 8,544 by 356
[tex]8544\div356=24[/tex]
[tex]854.40\div35.60=24[/tex]
Mrs. Hernandez worked "24 hours last week" by using the first options equation, we can find that answer.
Hope this helps.
When a number ,x, increases by 12% and then decreased by 12% then the new number will be?
Answer: The new number is 1.44% smaller than the original.
=========================================================
Explanation:
To increase by 12%, we involve the multiplier 1.12
Think of 1.12 as 100% + 12% = 1 + 0.12 = 1.12
We go from x to 1.12x
To decrease by 12%, we will use the multiplier 0.88 because 1 - 0.12 = 0.88
Think of it like a discount. If you save 12%, then you pay the remaining 88%
So 0.88*1.12x = 0.9856x
The value 0.9856 is smaller than 1, meaning that overall we have a net discount going on.
The discount rate is 1 - 0.9856 = 0.0144 = 1.44%
In other words, x ultimately goes down by exactly 1.44%
----------------
If you want to use an actual number to see an example, let's go for x = 100
Increasing 100 by 12% means we increase by 0.12*100 = 12
We go from 100 to 112
Then decreasing by 12% means the value goes down by 0.12*112 = 13.44 and drops to 112-13.44 = 98.56
The original value 100 becomes the final value 98.56
This is a percent decrease of (100-98.56)/100 = 0.0144 = 1.44%
At a sale, dresses were sold for $192 each. This price was 96% of a dress's original price. How much did a dress originally cost?
Answer:
it was 200
Step-by-step explanation:
srry if its wrong
HELP ASAP
What is the correct expanded form and value of (4/5)³ ?
Answer:
(4/5)³ = 4/5 * 4/5 * 4/5 = 64/125.Step-by-step explanation:
An exponent is a number that makes another number multiply itself.
If it's on a fraction, then we need to do this:
4/5³ = 4/5 * 4/5 * 4/5.It can be confusing.
Remember,
We are not adding.
Simplify.
c) [tex]\sqrt{25+10\sqrt{5} +5 }[/tex]
d) [tex]\sqrt{30+10\sqrt{5} }[/tex]
Answer:
[tex]5+\sqrt{5}[/tex]Step-by-step explanation:
Both are essentially same questions, considering 30 = 25 + 5.
Solving c)
[tex]\sqrt{25+10\sqrt{5} +5} =[/tex][tex]\sqrt{5^2+2*5*\sqrt{5} +(\sqrt{5} )^2} =[/tex][tex]\sqrt{(5+\sqrt{5} )^2} =[/tex][tex]5+\sqrt{5}[/tex]Solution:
Part-C)
√25 + 10√5 + 5=> √25 + 10 × √5 + 5=> √25 + 10 × 2.236 + 5 [√5 = 2.236 according to the table uploaded]=> √25 + 22.36 + 5=> √52.36 = 7.236Part-D)
√30 + 10√5=> √30 + 10 × √5=> √30 + 10 × 2.236 [√5 = 2.236 according to the table uploaded]=> √30 + 22.36=> √52.36 = 7.236Hoped this helped!
find sin(x) if cos(x) = -22/29
Answer:
sin(x) = ±(√357)/29 ≈ ±0.651533
Step-by-step explanation:
The relation between sine and cosine is ...
sin(x) = ±√(1 -cos(x)^2)
sin(x) = ±√(1 -(-22/29)^2) = √(1 -484/841) = √(357/841)
sin(x) = ±(√357)/29
_____
Additional comment
The sign of the cosine is negative, which places the angle in quadrant II or III. In quadrant II, the sine is positive; in quadrant III, the sine is negative. That is, we cannot tell which sign to apply from the information given.
(20, 21, 29) is a Pythagorean triple. We suspect a typo in the question: 22 is used where 20 or 21 is likely intended.
Someone help me pls
Answer:
1 5/8
Step-by-step explanation:
Andre ran 345 meters with the track club. If there are 1000 meters in one kilometer, how many kilometers did he run?
A. 0.0345 km
B. 3.45km
C. 34.5 km
D. 0.324km
All bots and links will be reported. Please do not message if this account did anything before as for this account has been given to me today.
Answer:
None of them are correct as the correct one is 0.345 (maybe you made a typo when typing the options)
Step-by-step explanation:
We can make:
[tex]\frac{345}{1000}[/tex] which equals 0.345 km
PLEASEPLEASEPLEASEPLEASE
A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 15 ft its width is 10 ft, and its surface area is 600 ft². (In the figure, h=height. Assume that the given surface area includes that of the top lid of the box.)
Answer:
The surface area of a rectangular box is the sum of the areas of the flat rectangular faces of the box. The height is the vertical side of the box. So the other sides are the length and width. Try to picture a box in your head, or you can draw it on paper.
Let x = length
Let y = width
Let h = height
Using these variables, we can write an equation that represents the surface formula.
A = 2(area of bottom face) + 2(area of front face) + 2(area of side face)
A = 2xy + 2xh + 2yh
This is general equation for surface area. All we need to do is plug in the known values into it and solve for h.
496 = 2(18)(8) + 2(18)h + 2(8)h
496 = 288 + 36h + 16h
Now it comes down to simple algebra. Isolate the h terms and solve for h from there.
208 = 52h
Divide both sides of the equation by 52 to get your height. I let you finish up here.
Step-by-step explanation:
A company's total cost, in millions of dollars, is given by C(t) where t is the time in years since the start-up date. The graph of C(t) is shown to the right. Find each of the following.a) The marginal cost,
b)
c)
d) Find C(t) and
The marginal cost that can be deduced from the information given about the company is 40e^-t.
What is a a marginal cost?Marginal cost simply means the change in production cost due to an additional unit produced.
From the complete question, the cost function is given as 60 - 40e^-t. Therefore, the marginal cost will be:
C'(t) = d/dt (60 - 40e^-t)
= d/dt (60) - 40 d/dt (etc)
= 0 - 40(-1)e^-t
= 40 e^-t.
Learn more about marginal cost on:
https://brainly.com/question/16615264
What is the slope intercept form of the equation of the line passing through (1,2) and (3,10).
Answer:
y = 4x - 2
Step-by-step explanation:
slope = (10 - 2)/(3 - 1) = 8/2 = 4
Let the equation be y = 4x + b
Sub (1, 2) into it,
2 = 4*1 + b
so b = 2 - 4 = -2
The equation is y = 4x - 2
help me please 20
0000
Pls help me pls pls pls pls pls
Answer:
-2, 0, d
refer the image attached
Answer:
d > -2
Graph :
Write an equation that goes through the points (18, 3) and (21, 1)
Answer:
[tex]2x+3y-45=0[/tex]
Step-by-step explanation:
The slope of the line that goes through (18, 3) and (21, 1) is
[tex]\frac{1-3}{{21-18}}=\frac{-2}{3}\\[/tex]
The slope of the line that goes through (18, 3) and (x, y) is
[tex]\frac{y-3}{{x-18}}[/tex]
So
[tex]\frac{y-3}{{x-18}} = \frac{-2}{3}\\-2(x-18)=3(y-3)\\-2x+36=3y-9\\2x+3y-45=0[/tex]
Brainliest if correct
Answer:
30
Step-by-step explanation:
(3+3³)
3+27
30
Answer:
[tex]30[/tex]
Step-by-step explanation:
[tex]3\cdot(1+3^2)\\\\3\cdot(1+9)\\\\3\cdot(10)\\\\30[/tex]
Remember to follow PEMDAS
What is an equation of the line that passes through the points (-6, 5) and (6, 7)?
Answer:
[tex]y=\frac{1}{6}x+6[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)\rightarrow(-6,5)[/tex] and [tex](x_2,y_2)\rightarrow(6,7)[/tex]
Determine slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}[/tex]
Use either ordered pair to find the y-intercept
[tex]y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b[/tex]
Final equation
[tex]y=\frac{1}{6}x+6[/tex]
Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number.
Seven times the product of negative six and a number.
What is the algebraic expression?
(Do not simplify.)
Please help me with this question
Answer:
13.5m/s
Step-by-step explanation:
formula is v=u + at
as given:
u=3m/s
a=1.5m/s²
t=7secs
v=3+1.5(7)
v=3 + 10.5
v = 13.5m/s
The unit for velocity is m/s
Answer:
a) 87
b) 13.5
Step-by-step explanation:
for the first question we've been given the equation and the parameters needed
so we just input the parameters
3a+4b when a is 17 and b is 9
therefore the answer is 3*17 + 4*9
51+36=87
second question
that's an equation of motion and we've been given all the parameters we also need so we just input the parameters In the equation
v=u+at
v=3+1.5*7
v= 3+10.5
v=13.5
(X+4)^1/2 =6
Please help
Answer:
32
Step-by-step explanation:
let both sides of equation be squared
((x+4)^½)² = 6²
x+4 = 36
x = 36-4
x = 32
Heather jogged 5 miles.
How many feet did she jog?
1 mi = 1760 yd, 1 yd = 3 ft
Enter your answer in the box
ft
Answer:
26400
Step-by-step explanation:
1 mi=1760 yd
5mi=8800yd
1yd=3ft
8800yd=26400ft
If Heather jogged 5 miles in terms of feet he jogged 26400 feet.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Heather jogged 5 miles.
Also given that 1 mi = 1760 yd and 1 yd = 3 ft.
Therefore, If Heather jogged 5 miles then he jogged 5×1760 yards and
5×1760×3 feet which is,
= 26400 feet.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ2
Hi everyone same as a while ago please help me with this :))) (with solution plzz) Thank you!
6.) Convert 820 cg to g.
7.) Convert 3.8 L to mL.
8.) Convert 56000 cL to L
9.) Convert 63 dL to mL.
10.) Convert 12 in to cm
11.) Convert 4 mi to ft.
12.) Convert 16 ft to cm.
(You don't have to answer all of them , Half of it is ok like 9-12 ) Thank you
Answer:
6. 8.2g
7. 3800 ml
8. 560 L
9. 6300 ml
10. 30.48cm
11. 21120 ft
12. 487.48cm
Step-by-step explanation:
820 ÷ 100
3.8 × 1000
56000 ÷ 100
63 × 100
12 × 2.54
4 × 5280
16 × 30.48
Please mark me as brainliest
Answer these questions about the steps of simplifying this rational expression:
Part A What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common factors.
Part B Write the quadratic expressions in the numerator and the denominator in factored form.
Part C Cancel the common factor of the numerator and the denominator to write the expression in simplified form.
Answer:
x²
Step-by-step explanation:
4x²-14x+6
x²-7x²+12x
=2×2×x×x-2×7×x+2×3
x×x×x-7×x×x+2×2×3
= -2+2
x×x
the 2s cancle each other
= x²
Order the side lengths , , , , and from least to greatest.
(Note that the figure is not drawn to scale.)
F
G
H
I
Answer:
1. FH, 2. GH, 3.IH 4. GI, 5. FG
Step-by-step explanation:
According to a certain geometric theorem, the smallest angle is always opposite to the smallest side of a triangle. Likewise, the largest angle is always opposite to the largest side. Using this theorem we can properly order the angles and sides.
Additionally, the interior degrees of a triangle will always be 180, and the interior of this quadrilateral is 360 degrees. Using this we can determine the missing angles.
180 - 75 - 55 = 50 (first missing angle)
180 - 59 - 63 = 58 (second missing angle)
The smallest angle would be 50 degrees and the largest 75.
The second smallest is 55 degrees, the third smallest is 58 degrees, the fourth smallest is 59 degrees, and the fifth is 63 degrees.
Now, one thing that seems a bit confusing is the fact that GH is opposite to 2 different angles, so how do we know WHICH angle to use to find its length. From what I understand, we should be able to find the average of the two angles across from this side to see what its place would be in terms of length.
63 + 50 = 56.5
This would make side GH larger than FH but less than HI
This is how I would solve the problem, and I think this is the correct order. Please let me know whether it turns out right.
Mark the formula/theorem below
The angle measures bigger means the opposite side of angle is bigger.Here
55<59<63<75So the order is
FH<IH<GI<GH<FGPlease answer the question in the picture
Answer:
(y-8) (y-8)Step-by-step explanation:
→ y² -16y +64
→ y²-8y-8y+64
→ y(y-8) -8(y-8)
→ (y-8) (y-8)
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high?
Answer:
[tex]\frac{2}{9\pi}ft^3/min[/tex]
Step-by-step explanation:
Given
[tex]\frac{dV}{dt}=2ft^3/min\\ \\\frac{dh}{dt}=?\\ \\V_{cone}=\frac{1}{3}\pi r^2h\\\\d=2r=3h\\\\\frac{d}{2}=r=\frac{3}{2}h\\\\h=2[/tex]
Calculation
[tex]V=\frac{1}{3}\pi r^2h\\ \\V=\frac{1}{3}\pi(\frac{3}{2}h) ^2h\\\\V=\frac{1}{3}\pi(\frac{9}{4}h^2)h\\ \\V=\frac{9}{12}\pi h^3\\ \\V=\frac{3\pi}{4}h^3\\ \\\frac{dV}{dt}=\frac{9\pi}{4}h^2\frac{dh}{dt}\\ \\2=\frac{9\pi}{4}(2)^2\frac{dh}{dt}\\ \\ 2=9\pi\frac{dh}{dt}\\ \\ \frac{2}{9\pi} =\frac{dh}{dt}[/tex]
Therefore, the rate that the height of the pile is changing when the pile is 2 feet high is [tex]\frac{2}{9\pi}ft^3/min[/tex].
Ram is three times as old as his sister Sudha. After three years, he will
be twice as old as Sudha. Find their present age.
Answer:
Step-by-step explanation:
Let's replace Ram with r and Sudha with s.
(r = 3s) + 3 = (r = 2s)
(r = 2x) = ( r = 3s - 3)
3s - 3 = 2x
3s - 1x = 2x
s = 3
If r = 3s and s = 3, then r = 3 x 3 = 9.
Ram is 9 years old and Sudha is 3 years old.
Answer:
age of ram = 9 years
and the age of sudha is 3 years
Step-by-step explanation:
let the present age of ram be x
and his sister sudha's present age be y
Ram is three times as old as his sister Sudha
so, x = 3y ----i)
After three years, he will be twice as old as Sudha.
so , x+3 =(y+3)2
=> x+3 = 2y+6 ----ii)
now putting the value of x in equation ii)
=> 3y+3 = 2y+6
=> 3y-2y = 6-3
=> y = 3 { the present age of sudha is 3 year}
now the age of ram = x = 3y
=> x = 3(3)
=> x = 9
1+2*3-4. Please answer
Answer:1(2x3)-4= 3
2x3= 6 -4=2+1=3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
2x3=6
1+6=7
7-4=3
write a linear equation that passes through the points(2,-2) and (0,1)
Answer:
Slope intercept: y = -3/2x + 1
Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]
Step-by-step explanation:
m = (change in y)/change in x)
But also
m = y_2 - y_1/x_2 - x_1
So lets substitute
m = 1 - (-2)/0 - (2)
Lets find the slope
m = 3/0 - (2)
m = 3/-2
m = -3/2 (Moved the negative)
Now we find the value of b using the equation of a line.
y = mx + b
y = (-3/2) * x + b
y = (-3/2) * (2) + b
-2 = (-3/2) * (2) + b
Now we find the value of b
Lets rewrite
-3/2 * 2 + b = -2
Cancel the CF of 2
-3 + b = -2
Move the terms without b to the right
b = -2 + 3
b = 1
Now we substitute our values of the slope and y-int into y = mx + b to find the equation.
y = -3/2x + 1
Answer:
[tex]y=\frac{-3}{2}x-1[/tex]
Step-by-step explanation:
Given the two points, we can use the slope formula to get the slope of our equation.
[tex]\frac{y_2-y_1}{x_2-x_1}=m[/tex]
Plug in what we know
[tex]\frac{(1)-(-2)}{0-2}=m[/tex]
[tex]m=\frac{-3}{2}[/tex]
[tex]y=\frac{-3}{2}x-b[/tex]
Plug in one of the points given and solve to find our y-intercept [b]
[tex]-2=\frac{-3}{2}(2)-b[/tex]
[tex]b=1[/tex]
(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)
Final equation
[tex]y=\frac{-3}{2}x-1[/tex]