Answer:
b
Step-by-step explanation:
8
There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?
Answer:
.8L
Explanation:
Logic
The liters of water left are 0.8 liters.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The quantity of water in a water bottle is 1 liter.
The amount of water Tom drank is 200 milliliters.
Let x be the amount of water left in the bottle.
The liter has to be converted into milliliters.
1 liters = 1000 milliliters
The equation formed is,
1000 - 200 = x
x = 1000 - 200
x = 800 milliliters.
The water left in the water bottle is 800 milliliters.
1000 milliliters = 1 liters
800 milliliters = 0.8 liters
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A rectangle or prism has dimensions of 2 cm x 2 cm x 3 cm what is the surface area
Answer:
32 cm²
Step-by-step explanation:
SA = 2(lw + lh + hw)
= 2(2x2 + 2x3 + 3x2)
= 2(4 + 6 + 6)
= 2(16)
= 32 cm²
1. Multiply the following polynomials to write an equivalent expression.
Part A: -7x2y2 (8x2y – 5xy + 11xy2 – 31)
Part B: (t3 – 5t) E+2 – 3t)
Part C: (4x2 – 7x + 5)(2x - 5)
Part D: (3m2 - 5m + 2)2
Answer/Step-by-step explanation:
A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]
[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)
[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)
B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]
[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)
[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]
[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]
Combine like terms
[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (note: -12/5 - 5/4 = -73/20)
C. (4x² - 7x + 5)(2x - 5)
4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)
8x³ - 20x² - 14x² + 35x + 10x - 25
Combine like terms
8x³ - 34x² + 45x - 25
D. (3m² - 5m + 2)²
= (3m² - 5m + 2)(3m² - 5m + 2)
= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)
= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4
Combine like terms
= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4
= 9m⁴ - 30m³ + 37m² - 20m + 4
The probability of a student passing
an examination is 2/3
If the student
takes three examination, what is the
Probability that he will not
pass
any of them.
===============================================
Explanation:
2/3 is the probability of passing a test, so 1/3 is the probability of failing
Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%
The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.
-------
Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27
fatima bought an xbox game that is 38.00 plus 9% sales tax what is the sales tax on the xbox game that fatima purchased answer
An open top box is to be made by a 24 in by 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?
Answer:
X= -12 +6√10
X= 6.973
Step-by-step explanation:
Volume of the box= (36-2x)(24-2x)x
Volume of the box
=( 864 -96x -4x²)x
But 864 -96x -4x²
=216 - 24x-x²
Solving for x quadratically
X= (24+12√10)/-2
X= -12 -6√10
X= -30.97
Or
X= (24-12√10)/-2
X= -12 +6√10
X= 6.973
X will definitely be a positive number
So X= -12 +6√10
X= 6.973
Increasing or decreasing the side length of the square that gives the
maximum volume, gives a volume that is less than the maximum.
The side length of the cut out square to get a box with the maximum volume is approximately 4.71 in.Reasons:
The given dimensions of the box = 24 in. by 36 in.
Let x represent the dimensions of the square removed from the corners, we have;
Width of box = 24 - 2·x
Length of box = 36 - 2·x
Height of the box = x
Volume of a box = Width × Length × Height
Therefore;
Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x
At the maximum or minimum point of the volume, we have;
[tex]\displaystyle \frac{dV}{dx} = \mathbf{ \frac{d}{dx} \left(4 \cdot x^3 - 120 \cdot x^2 + 864 \cdot x \right )} = 0[/tex]Which gives;
12·x² - 240·x + 864 = 0
x² - 20·x + 72 = 0
Which gives;
[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]
At x = 10 + 2·√7, we have;
[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]
2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard
Therefore, (10 + 2·√7) is too long to be cut from the cardboard
At x = 10 - 2·√7, we have;
V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3
Therefore;
The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches ≈ 4.71 inches
The size of the square to be cut out each corner is x ≈ 4.71 inchesLearn more here:
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For income tax purposes, a man uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. A man assumes that he can use the machine for years. The following graph shows the value of the machine over the years. What loss in value occurred during the first year?
Answer: $500
Step-by-step explanation:
The vertical axis of the graph represents the value of the copy machine and the horizontal axis represents the years.
Using the line, one can see that in the first year, the value of the machine went from $7,000 to $6,500.
The loss in value is therefore;
= 7,000 - 6,500
= $500
The needed graph is attached.
Angles, angles everywhere! Big ones, little ones, right
ones too! But this angle is something new. It has two
rays that meet at a vertex, and it measures 180
degrees. How complex! What angle am I? Draw me.
Answer:
Straight angle
<----------------------------->
You can determine if an angle is a straight angle only if it is 180 degrees. You can also draw it by drawing a straight line and drawing an arrow facing outward at each end.
Someone help me on this.
Answer:
[tex]-57-39i[/tex]
Step-by-step explanation:
So we have the expression:
[tex](7+2i)(-9-3i)[/tex]
FOIL:
[tex]=7(-9)+7(-3i)+2i(-9)+2i(-3i)[/tex]
Simplify:
[tex]=-63-21i-18i-6i^2[/tex]
Recall that i² is just -1. Thus:
[tex]=-63-21i-18i-6(-1)[/tex]
Simplify:
[tex]=-63-21i-18i+6[/tex]
Combine like terms:
[tex]=(-63+6)+(-21i-18i)[/tex]
Add:
[tex]=-57-39i[/tex]
And we're done!
What two numbers should be placed in the blanks below so that the difference between the
consecutive numbers is the same?
13,_,_,34
Answer:
20,27
Step-by-step explanation:
let 13,a,b,34 be consecutive numbers.
a=13
l=34
n=4
l=a+(n-1)d
34=13+(4-1)d
34-13=3d
21=3d
d=21/3=7
a=13+7=20
b=20+7=27
Answer:
20, 27
Step-by-step explanation:
The difference 34-13 = 21 must be divided into three equal parts. Each is 21/3 = 7.
The numbers are 13+7 = 20, 20+7 = 27. As a check, 27 +7 = 34
The missing numbers are 20 and 27.
Express each rational number in decimal form.
[tex] \frac{3}{4} [/tex]
Answer:
.75
Step-by-step explanation:
there is only 1 number
0.75
The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn't come out evenly, you can stop after a certain number of decimal places and round off.
Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 19 total hours and must earn a minimum of $270. If Brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.
Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.
$270-$252=$18, he needs to earn $18 more from clearing tables.
$18÷9=2, so the minimum number of whole hours clearing tables is 2
Skip count by twos.
30,_ _ _ _ _ _ _ _ _,50.
Write the equation of the line PERPENDICULAR to y = 3/2x + 6 that passes through the point (-3, 4).
Answer:
Step-by-step explanation:
perp. -2/3 slope
y - 4 = -2/3(x + 3)
y - 4 = -2/3x - 2
y = -2/3x + 2
What is 30/35 in simplest form?
Answer: 6/7
Step-by-step explanation:
3. Round 9995.2 to the nearest ten. Explain in your
own words the reasoning behind why we round
the number the way we do. Use a number line to
support your explanation
Answer:
10000
Step-by-step explanation:
First, highlight parts of the question. Since it says round to the nearest ten, draw a number line to start. Start by drawing a number line from 9990 to 10000. Whenever a number has the digit from 5 till any number less than 10, you round up. If the number you are trying to round to any digit is less than 5, then you can round down. Since the part of the number that is important for the question is 5.2, we round above. You get 10000 from this.
Complete the table
30x – 6y = -6x2
Answer:
-0.5
Step-by-step explanation:
30x - 6x = -6(2)
24x -12
24 24
x = -.5
Jamal owes $424.04 on his credit card. He returns two items, one for $49.95 and the other for $50.42.
Then he makes purchases of $39.19 and $37.41. What is the new balance on the card?
Answer:
$400.27
Step-by-step explanation:
owes $424.04
returns an item for $49.95
-424.04 + 49.95 = -374.09
he now owes $374.09
returns an item for $50.42
-374.09 + 50.42 = -323.67
he now owes $323.67
makes a purchase of $39.19
-323.67 - 39.19 = -362.86
he now owes $362.86
makes a purchase of $37.41
-362.86 - 37.41 = -400.27
he now owes $400.27
Find a unit vector that is orthogonal to both i + j and i + k.
Answer: i - j - k
Step-by-step explanation:
Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.
<1,1,0> x <1,0,1>
[tex]det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )[/tex]
the determinate of the matrix: <1,-(1),-1>
or: i - j - k
a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate
Answer:
1 1/14 lbs
Step-by-step explanation:
We can use ratios to solve
2/3 crate 1 crate
----------------- = -----------------
5/7 lb x lbs
Using cross products
2/3x = 5/7 *1
Multiply each side by 3/2
3/2 * 2/3 x = 3/2 * 5/7
x = 15/14
x = 1 1/14
Answer:
[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]
Step-by-step explanation:
[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]
The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.
|x______ | = _______
x = __________ (smaller number here)
x = _______ (larger nember here)
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Answer:
[tex]|x - 85| = 12[/tex]
[tex]x = 73 \ (smaller\ number )[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
Step-by-step explanation:
From the question we are told that
The grade is [tex]k = 85\%[/tex]
The variation is [tex]v = 12 \%[/tex]
Generally the absolute value equation is mathematically represented as
[tex]|x - 85| = 12[/tex]
=> [tex]x -85 = \pm 12[/tex]
So
[tex]x = 85 + 12[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
And
[tex]x = -12 + 85[/tex]
=> [tex]x = 73 \ (smaller\ number )[/tex]
What is the measure of r
Answer:
The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°
Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?
3 tests at 75% each = 3 x 75 = 225 total points
First two tests = 79 + 84 = 163
Third test needs to be at least: 225 - 163 = 62%
So any score less than 62 would get you into trouble.
Can someone please help me on this one!
Answer:
The answer is (1,-1)
Step-by-step explanation:
The best approach for this problem is to plug in the coordinates into the given inequality.
[tex]7x-3y\geq 10\\[/tex]
(3,4) ------> [tex]7(3)-3(4)=9[/tex]
9 is less than 10 so, we can rule this one out.
(1,0) -------> [tex]7(1)-3(0)=7[/tex]
7 is less than 10 so, we can rule this one out.
(1,2) -------> [tex]7(1)-3(2)=1[/tex]
1 is less than 10 so, we can rule this one out.
(1,-1) -------> [tex]7(1)-3(-1)=10[/tex]
10 is equal to 10, so this is the answer.
Hope this helps!
As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions
if 7x - 3y > 10 then
7x > 10 +3y
Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6
then by substitution
7 must be > 10+ 3*6
or 7x must be > 28
or x must be > 4
So all pairs such that x is > 4 and y = 6 are solutions.
I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x to derive appropriate pairs
Solve for x.
16 = -2x - 1
x = -8
x = -7
x = 7
x = 8
Step-by-step explanation:
16=-2x-1
17=-2x
x=-17/2
x=-8.5
(this one isn't in the correct order but it's one of the answers ¯\_(ツ)_/¯
16 = -2x - 1
-8=x-1
-7=x
x=-7
Answer as a fraction (please help)
is is 6 2/7 rational or irrational
is -19 rational or irrational
is -√100 rational or irrational
Step-by-step explanation:
6 2/7is rational
-19is rational but next I dont know
Find the value of x.
X=8
X=10
X=16
X=20
Answer:
D. 20Step-by-step explanation:
Find the required diagram to the question in the attachment.
From the diagram it can be seen that the distance of the lines projecting from the centre of the circle to the line segment is equal i,e they are both 8. This means that the length of both chords given will be equal. For the known chord length, it can be seen that the line perpendicular to the chord cuts them at the centre. and since both sides of the chord are parallel, the other sides too will be 10 making the total length to be 10+10 = 20.
Since the length of the known chord is equal to the length of the unknown chord x, hence, the value of x will also be 20
Answer:
D. x=20
Step-by-step explanation:
correct on EDGE2021
Which step is incorrect when solving the equation 2(x+9)=4(x+7)+2?
Choose the first step that made an error.
1. 2(x+9)=4(x+7)+2
2. 2x+18=4X+28+2
3. 2x+18=4x+26
4. -8=2x
5. -4=x
(i think it's step 3)
Answer:
3. 2x+18=4x+26
Step-by-step explanation:
2(x+9)=4(x+7)+2
2x+18=4x+28+2
2x+18=4x+30
The step that made an error in solving this linear equation is step 3.
Hope this helps ;) ❤❤❤
Solve 16x + 9 = 9y – 2x for y.
y =