Answer:
see below
Step-by-step explanation:
A
Add the students who passed french, german, both
add 17+19+11 = 47
Subtract this from 55 to get b
b = 55-47 =8
b =8
B
P( passed french and german)
= number that passed french and german / total
= 19/55
P( french or german) =
= number that passed french or german / total
= (17+11)/55 =28/55
James is working at a place that ships boxes. Each box is rectangular prism that measures 2 ft long, 3 ft wide, and 2 ft tall. He is loading a small trailer that has 396 cu ft of space. What is the maximum number of boxes he can fit inside the trailer?
Answer:
33
Step-by-step explanation:
2x3x2=12 396/12=33
Can some please help me with this question? And can you show your work too? I will mark the best answer Brainliest
Answer:
Finding the vertex by completing the square
1) The vertex = (4/3, -4/3)
2) The vertex = (-1/2, 36)
3) The vertex = (2/3, 26/3)
Finding the value of x by completing the square
1) x = 1 or -4
2) x = 3/2 or -7/2
3) x = 1 or -3
Step-by-step explanation:
Finding the vertex by completing the square
The vertex form of the quadratic equation y = ax² + bx + c is written as follows;
y = a(x - h) + k
Therefore, we have;
Y = 3·x² + 4 - 8·x = a(x - h)² + k
Hence, a = 3
Which gives;
3×(x² - 2·x·h + h²) + k
Hence, we have 3×2×h = 8
h = 8/6 = 4/3
The constant term = k
We note that 3 × h² + k = 4
∴ k = 4 - 16/3 = -4/3
The vertex form is therefore;
Y = 3(x - 4/3)² - 4/3
The vertex = (4/3, -4/3)
2) Where Y = 4·x² + 4·x + 36
a = 4
4× -2·h = 4
∴ h = 4/(4 × (-2)) = 4/-8 = -1/2
Also, 4 × h² + k = 36
Which gives;
4 × (-1/2)² × k = 36
k = 36
The vertex form becomes
y = 4(x - (-1/2)) + 36
The vertex = (-1/2, 36)
3) Where Y = -3·x² + 4·x + 10, we have
a = -3
3×2×h = 4
∴ h = 4/(2×3) = 2/3
a×h² + c = k
-(3)×(2/3)² + 10 = 26/3
Which gives;
Y = -3(x - 2/3) + 26/3
The vertex = (2/3, 26/3)
To find the value of x by completing the square, we have;
1) 2·x² = -6·x + 8
2·x² + 6·x = 8
2·(x² + 3·x) = 8
x² + 3·x = 8/2 = 4
x² + 3·x + (3/2)² = 4 + (3/2)² = 25/4
(x + 3/2)² = 25/4
∴ x + 3/2 = ±5/2
x = 5/2 - 3/2 or -5/2 - 3/2
x = 1 or -4
2) 8·x² + 16·x = 42
8·(x² + 2·x) = 42
x² + 2·x = 42/8 = 21/4
x² + 2·x + 1 = 21/4 + 1 = 25/4
(x + 1)² = 25/4
x + 1 = √(25/4) = ± 5/2
x = 5/2 - 1 or -5/2 - 1
∴ x = 3/2 or -7/2
3) -x² + 2·x = -3
-x² + 2·x = -3
-1×(-x² + 2·x) = -1 ×-3 = 3
x² - 2·x = 3
x² - 2·x + 1 = 3 + 1 = 4
(x - 1)² = 4
x - 1 = √4 = ±2
∴ x = 2 - 1 or -2 - 1
x = 1 or -3
In △ABC, AB = 13.2m,
BC = 6.9m and ∠ACB = 90°. H lies on AC such that
∠BHC = 46°. Find
(i) ∠ABH
(ii) The length of AH
Answer:
(i) ∠ABH = 14.5°
(ii) The length of AH = 4.6 m
Step-by-step explanation:
To solve the problem, we will follow the steps below;
(i)Finding ∠ABH
first lets find <HBC
<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)
46° + <HBC + 90 = 180°
<HBC+ 136° = 180°
subtract 136 from both-side of the equation
<HBC+ 136° - 136° = 180° -136°
<HBC = 44°
lets find <ABC
To do that, we need to first find <BAC
Using the sine rule
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
A = ?
a=6.9
C=90
c=13.2
[tex]\frac{sin A}{6.9}[/tex] = [tex]\frac{sin 90}{13.2}[/tex]
sin A = 6.9 sin 90 /13.2
sinA = 0.522727
A = sin⁻¹ ( 0.522727)
A ≈ 31.5 °
<BAC = 31.5°
<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)
31.5° +<ABC + 90° = 180°
<ABC + 121.5° = 180°
subtract 121.5° from both-side of the equation
<ABC + 121.5° - 121.5° = 180° - 121.5°
<ABC = 58.5°
<ABH = <ABC - <HBC
=58.5° - 44°
=14.5°
∠ABH = 14.5°
(ii) Finding the length of AH
To find length AH, we need to first find ∠AHB
<AHB + <BHC = 180° ( angle on a straight line)
<AHB + 46° = 180°
subtract 46° from both-side of the equation
<AHB + 46°- 46° = 180° - 46°
<AHB = 134°
Using sine rule,
[tex]\frac{sin 134}{13.2}[/tex] = [tex]\frac{sin 14.5}{AH}[/tex]
AH = 13.2 sin 14.5 / sin 134
AH≈4.6 m
length AH = 4.6 m
Anybody know the answer?
Yes!
This does represent a function because all numbers in this table are real numbers.
Integers and whole numbers are apart of real numbers.
Therefore you do not have to state why this is not a function because it certainly is!
Express 29 out of 40 as a percentage
Answer:
72.5%
Step-by-step explanation:
To express a value as a %:
value/whole x 100 = 29 / 40 x 100
This gives you 72.5%
Hope this helps
Choose the equation you would use to find the altitude of the airplane. tan70 = 800/x sin70 = x/800 tan70 = x/800
Answer: tan(70)=x/800
Step-by-step explanation:
Since we are looking at the altitude and x and 800 are given, we will need tangent. Tangent is opposite/adjacent. We can eliminate sin(70). Between our 2 tangent choices, the answer is tan(70)=x/800. Tan(70)=800/x is very close but incorrect. 800/x is adjacent/opposite. That is not a trigonometric function. We are looking for opposite/adjacent.
HELPPP PLEASEE l
The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline.
The graph shows the distance, y, that car P traveled using x gallons of gasoline
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
which is a valid proportion? 4/18=6/27 4/6=16/36 3/4=9/12 5/9=8/12 Check all that apply
Answer:
Given
Hope it helps..
Step-by-step explanation:
The options that apply are:
4/18= 6/27
3/4= 9/12
How to check:
Multiple the middle two terms
Then divide the product by one of the outer terms
If you get the other outer term, its a valid proportion
Which line has a slope of 0? A: x = 1 B: 3y + 6x = 0 C: y = x D: y = -5
Answer:
D) y=-5
Step-by-step explanation:
..............
Which circle C shows a chord that is not a diameter?
Circle C is shown. A line is drawn from one side of the circle to the other side and goes through point C.
Circle C is shown. A line is drawn on the outside of the circle and intersects the circle at one point.
Circle C is shown. A line is drawn from point C to a point on one side of the circle.
Circle C is shown. A line goes from one point on the circle to another point on the circle.
Answer:
The answer is option D
Step-by-step explanation:
Just got it right on edge :)
Answer:
d
Step-by-step explanation:
Find the radius and center of the circle given by the equation below.
(x-6)2 + (y + 4)2 = 7
Ore 17 and center at (-4.6)
or= 7 and center at (6-4)
or=7 and center at (-6.4)
or= 7 and (
6-4)
Answer:
center (6,-4)
radius = √7 unit
Step-by-step explanation:
Mathematically, the equation of a circle can be written as follows;
(x-a)^2 + (y-b)^2 = r^2
Where (a,b) represents the center of the circle with r representing the radius of the circle.
Now looking at the values in the question, we can clearly see that a = 6, while b represents -4.
The radius of the circle is √7
So the circle center is (6,-4) while √7 is the circle center
Approximate the value of positive square root 5 to the nearest hundredth
Answer:
2.2
Step-by-step explanation:
Please help, I need this answer
Answer:
6.4
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]
Hope this helps!
Answer:
To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4
Answer: is approx. 6.4Simplify: (2x2 − 9x + 3) + (−7x2 + 4x − 2)
Answer:
-5x^2-5x=+1
Step-by-step explanation:
find the coordinate of H' after a Glide reflection of the triangle translation 3 units up and 1 unit right then a reflection across the x-axis. answer in (a,b).
Part 1a
Answer:
H' = (4, -2)
Step-by-step explanation:
Translating point H three units up and one unit right places it at (4, 2).
Then after a reflection across the x-axis, the y value is reversed, and the point is placed at (4, -2)
Rewrite
y +2>1/3 (6x – 9) to isolate the yterm.
Answer:
[tex]y>2x-5[/tex]
Step-by-step explanation:
[tex]y +2>1/3 (6x-9)[/tex]
Expand 1/3(6x-9).
[tex]y +2>6/3x-9/3[/tex]
[tex]y +2>2x-3[/tex]
Subtract 2 on both sides.
[tex]y +2-2>2x-3-2[/tex]
[tex]y>2x-5[/tex]
The rewritten form of y +2 > 1/3 (6x – 9) where the y-term us isolated is; y > 2x -5
To isolate the y-term;
The following operations are carried out;
y +2 >1/3 (6x – 9)y +2 > 2x – 3By finally isolating y; we have;
y > 2x -5
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The equation of the line is ___
Answer:
Since the slope is -2 and y-int. is 3 the slope-intercept form is y = -2x + 3 which in standard form is 2x + y = 3.
Answer:
y = -2x + 3
Step-by-step explanation:
→ We know the slope so we can automatically plug that into the y = mx + c formula so,
y = -2x + c
→ Now we substitute in the coordinates (0,3) to find the c value and therefore complete the equation
y = -2x + c
3 = ( -2 × 0 ) + c ⇔ 3 = 0 + c ⇔ c = 3
y = -2x + 3
You are hiking on a trail that leads down from the top of a mountain. At 11 A.M. You are at an elevation of 5400 feet. At 3 P.M. You are at an elevation of 3800 feet. What is your mean hourly change in elevation?
Step-by-step explanation:
You hiked 5400 - 3800 = 1600 feet in 4 hours so the mean change is 1600 / 4 = 400 ft/hour.
Can someone help? It’s about 2 column proofs
Step-by-step explanation:
1. AB = BC (B is the midpoint of AC)
2. DE = EF (E is the midpoint of DF)
3. EB is common
4. ∠ABE = ∠CBE; ∠BED = ∠BEF (EB⊥AC, EB⊥DF)
5. ΔDEB ≅ ΔFEB (RHS)
6. DB = FB (corresponding ∠s of ≅ Δs)
7. ∠EFB = ∠CBF; ∠EDB = ∠ABD (alternate interior angles, AC║DF)
8. ΔABD ≅ ΔCBF (SAS)
What is the volume of the rectanguler prism?
Answer:
33
Step-by-step explanation:
V = 3*2 * 5 1/2
V = 6 * 11/2
V = 33
Answer:
V=whl
Step-by-step explanation:
V=51/2 * 3*2
V=153
Log(4x-10)32=5 solution?
Answer:
x = 3
Step-by-step explanation:
log(4x - 10)32 is not properly formed; it's also ambiguous.
If you mean to say that (4x - 10) is the base, then you have to do the rather awkward typing shown below:
log 32 = 5
(4x - 10) (where (4x - 10) is assumed to
be the base)
log 32
(4x - 10)
Then (4x - 10) = (4x - 10)^5
or 32 = (4x - 10)^5, or
2^5 = (4x - 10)^5
which tellus us that 2 = 4x - 10, or 4x = 12, or x = 3
An arithmetic sequence has this recursive formula. a1=9 and 1-3 .
The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.
Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example, 1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term) and common differene d = 2- 1 = 1.
Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.
Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Learn more about arithmetic progression here:
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What is the standard equation of the circle on the graph?
A. (x+2)^2 + (y-3)^2 = 2
B. (x-2)^2 + (y+3)^2 = 2
C. (x-2)^2 + (y+3)^2 = 4
D. (x+2)^2 + (y-3)^2 = 4
Answer: D
Step-by-step explanation:
The equation would be (x+2)^2 + (y-3)^2 = 4 if I did it right. (Sorry if it’s wrong!)
Answer = D :)
Step-by-step explanation:
Which data set is least Likely to resemble a normal distribution?
Look at picture
Answer: B) The heights of girls who live on a certain street in the city of Buffalo
Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.
Container X contained 1200g of sand.Container Y contained 7.2kg of sand.After an equal amount if sand was removed from each container,Container Y had 7 times as much sand as container X.how much sand was removed from each container?
Find the surface area of this triangular prism shown below
Answer:
Step-by-step explanation:
area of side triangles=2(1/2×6×4)=24 units²
area of 3 rectangles=6×7+2(5×7)==42+70=112 units²
or=(6+5+5)×7=16×7=112 units²
Total surface area=24+112=136 units²
which of these statements us true for f(x)=3•(9)^x
Answer:
C
Step-by-step explanation:
The y-intercept is at x=0, y=3.
knlkn/l,kjn.kj.njkbjkb,.bgj,hjbhb b. ,.
Answer:
hmmmmmmmmmmmmmmmmm
Step-by-step explanation:
egfrggggggdfgd
djdgg
gfhdst
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the measure of angle b in the image below.
Answer:
complementary, b = 90 - 37 = 53
step-by-step explanation:
Answer:
see below
Step-by-step explanation:
These angles are complementary.
b + 37 = 90
b = 53°
Please help……………………………………!!!!!!!!!
Answer:
4 k^4
Step-by-step explanation:
(64 k^12) ^ 1/3
We know (ab)^c = a^c * b^c
64 ^ 1/3 k^12^1/3
4 * k^12^1/3
We know a^b^c = a^(b*c)
4 k^(12*1/3)
4 k^4