Answers
taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2. Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).
[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]
Check the picture below.
Related Questions
-10 + 2t = -20 16t + 17t
Answers
t=2/61
1 Rearrange terms
2
Multiply the numbers
3
Combine like terms
4
Add
10
to both sides
5
Simplify
6
Add
303t
to both sides
7
Simplify
8
Divide both sides by the same factor
9
Simplify
H E L P M E P L I Z
In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.
23z+19=3(5z-9)+8z+46
15y+32=2(10y-7)-5y+46
Answers
The 2 equations are classified as Identities because both sides remain the same for all values of z.
How to Classify Equations?1) We are given the equation;
23z + 19 = 3(5z - 9) + 8z + 46
Let us try z = 0
23(0) + 19 = 3(5(0) - 9) + 8(0) + 46
19 = -27 + 46
19 = 19
Let us try z = 5;
23(5) + 19 = 3(5(5) - 9) + 8(5) + 46
134 = 48 + 40 + 46
134 = 134
Thus, this is an identity as both sides remaining the same for all values of z.
2) We are given the equation;
15y + 32 = 2(10y - 7) - 5y + 46
At y = 0, we have;
15(0) + 32 = 2(10(0) - 7) - 5(0) + 46
32 = -14 + 46
32 = 32
Let us try y = 2;
15(2) + 32 = 2(10(2) - 7) - 5(2) + 46
62 = 26 - 10 + 46
62 = 62
This is an identity as both sides remaining the same for all values of z.
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how to find the 3 sides
Answers
The angle of triangle are ∠A = 86, ∠B = 55, ∠C = 39. The side of the triangles are a = 0.99, b = 0.81, c = 0.62.
What is a law of sine?Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.
[tex]\dfrac{sin A}{a} = \dfrac{sin B}{b} = \dfrac{sin C}{c}[/tex]
We have given angles of the triangle as
∠A = 86
∠B = 55
∠C = 39
So,
[tex]\dfrac{sin 86}{a} = \dfrac{sin 55}{b} = \dfrac{sin 39}{c}[/tex]
Now,
a = 0.99
b = 0.81
c = 0.62
The side of the triangles are a = 0.99, b = 0.81, c = 0.62.
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En 2018 la empresa SAC-OLC fabrico 24000 ollas, si cada dia se fabricaron 80 ollas ¿cuantos dias no se trabajaron en la empresa?
Answers
Usando proporciones, hay que no se trabajaron en 65 dias durante el año de 2018 en la empresa SAC-OLC.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e los problemas pueden ser resolvidos con una regla de três.
En este problema, hay que se fabricaran 24000 ollas en el año de 2018, con una taja de 80 ollas al dia. Así, el número de dias trabajados es dado por:
n = 24000/80 = 300.
El año de 2018 tuvo 365 dias, así, el número de dias no trajados fue de:
365 - 300 = 65.
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A rescue mission is being conducted using a plane to drop supplies and medical personnel. A helicopter
is also sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the
helicopter flies 200 mph, and they leave at the same time, how far away is the rescue site if the
helicopter arrives 1 hour after the plane arrives?
If t represents the time that the plane flies, which of the following equations could be used to solve the
problem?
400/t = 200/(t+1)
400t = 200(t+1)
400t = 200t+1
Answers
400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
A helicopter is sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the helicopter flies 200 mph, and they leave at the same time.
Let's suppose the plane takes t hours
We know,
Distance = speed×time
400×t = 200(t + 1)
or
400t = 200(t + 1)
After solving we get:
t = 1 hour
Distance = 400×1 = 400 miles
Thus, 400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
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31 32 33 34
Which polynomial function could be represented by the graph below?
16
14
42
10
8-6
6 8 X
O f(x) = x³ + x² - 6x
O f(x)=x²-x² - 6x
4
1:00:00+
bocchette
ANLAT
K
C
Answers
The polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x
How to determine the polynomial?The attached graph represents the missing part of the question
From the attached graph, the x-intercepts of the graph are:
x1 = -3
x2 = 0
x3 = 2
The equation of the graph is then calculated as:
f(x) = (x - x1)(x - x2)(x - x3)
This gives
f(x) = (x + 3)(x - 0)(x - 2)
Expand
f(x) = x(x² + 3x - 2x - 6)
Evaluate
f(x) = x(x² + x - 6)
Expand
f(x) = x³ + x² - 6x
Hence, the polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x
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what is 1/4×2/5÷1/3 as a fraction
please help
Answers
Answer:
3/10
Step-by-step explanation:
Please give brainliest!
hope this helps :)
the first step is to multiply 1/4 and 2/5
1/4 times 2/5 = 2/20
you figure this out by multiplying the numerators and denominators.
next, we solve 2/20 ÷ 1/3
we do this by taking the reciprocal of 1/3, which is 3/1, and then multiplying the fractions
2/20 times 3/1 = 6/20
6/20 = 3/10
Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.
Answers
Answer:
It would be 35/36
Step-by-step explanation:
so if you did like 1+1, 1+2, 1+3....2+1,2+2, 2+3 yada yada
the only possible number combo that would equal twelve is 6+6 and there is 36 possible combos so your answer is 35/36
- a former algebra 2 student
please help with all of question 5
Answers
Volume of a right cone with base radius r cm and height h cm :
V = 1/3 π r² h cm³
Surface area :
A = (π r² + π r √(h² + r²)) cm²
Volume of a sphere with radius r cm :
V = 4/3 π r³ cm³
Surface area :
A = 4 π r² cm²
Volume of a cuboid with dimensions r cm × r cm × h cm :
V = r² h cm³
Surface area :
A = 2 r² + 4 r h
a. If the cone and sphere have the same volume, then
1/3 π r² h = 4/3 π r³ ⇒ h = 4r
b. If the area of the cuboid is 98 cm², then
2 r² + 4 r h = 98 ⇒ r (r + 2 h) = 49
c. Since h = 4r, substituting this into the equation from (b) gives
r (r + 8 r) = 9 r² = 49 ⇒ r² = 49/9 ⇒ r = 7/3
d. With r = 7/3, we have
h = 4 × 7/3 = 28/3
and so the volume of the cuboid is
V = (7/3 cm)² (28/3 cm) = 1372/27 cm³
PLEASE HELP ME!!!!!!!!!!!!!!!
Answers
Answer:
hypotenuse(h)^2 = 3^2 + 7^2
h^2 = 9 + 49
h = √58
h = 7.6
do these ratios form a proportion?
Answers
Answer:
No, because both of them will never be able to match; become equivalent. You would have to multiply 2 different numbers to make them match, meaning they would not be proportional. For a comparison to be proportional, the ratio you are trying to simplify to must be achieved by multiplying 2 numbers from the previous ratio by one LCD.
[tex]\frac{3\cdot 4}{7 \cdot 3} = \frac{12}{21}[/tex]
They are able to make 12/21, but that does not mean they are proportional.
Can someone please help me with this?
Answers
Answer:
Answer Option C
Step-by-step explanation:
They make a big plus sign, PLUS=PERPENDICULAR
5. x = 5,- ²/3, √2
help pls
Answers
Answer: 2. 5. f(x)=x²-5; vertically stretched by a factor of 4, followed by a translation 3 units to the right. 4(x²-5). 4((x-3)²-5) g(x)= 4(x-3)²-20.
Step-by-step explanation:
What is the slope of the line containing (-2,5) and (4, -4)?
O A. -2
O B.
3
2
O c. 2
O D.
3
2
Answers
Answer:
-3/2
Step-by-step explanation:
See attached image
Answer:
[tex]m=\frac{-3}{2}[/tex]
Step-by-step explanation:
m = slope
[tex]m=\frac{-4-5}{4--2}[/tex]
[tex]m=\frac{-9}{6}[/tex]
[tex]m=\frac{-3}{2}[/tex]
What number can be used to complete the volume statement for the cone?
a cone with height 4 meters and diameter 3 meters.
volume =
Answers
Answer: 9.42 cu. meters
Step-by-step explanation:
V= 1/3 x TT x r^2 x height
TT (pi) = 3.14
r^2 is 1/2 diameter = 1.5
height = 4
V = 1/3 x 3.14 x 1.5^2 x 4
V= 1/3 x 3.14 x 2.25 x 4
V = 9.42 cu. meters
Which regular polygon has a rotation of 240 degree to carry the polygon onto itself?
Answers
The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is the equilateral triangle.
The missing part of the questionOptions
Equilateral triangle
Octagon
Rectangle
Pentagon
How to determine the polygon?A polygon that can carry itself onto itself after a rotation of 240 degrees must obey the following rule:
Angle of rotation = 360/Sides
Next, we test the options:
Option (a) equilateral triangle
Angle of rotation = 360/3
Evaluate
Angle of rotation = 120
Next, we list the multiples of 120
120, 240, 360.....
See that 120 is a factor of 240.
This means that the equilateral triangle would be rotated onto itself when rotated by 240 degrees.
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1. Which is NOT a benefit of direct deposit? (1 point)
The money is available as soon as your employer makes the transfer.
You do not need to drive to the bank to make a deposit.
You can plan when you are paying bills.
You can avoid having a hold placed on when funds are available.
Answers
Answer:
d
Step-by-step explanation:
the statement "you can avoid having a hold placed on when funds are available is noat a benefit of the direct deposit
Find the equation of the line shown.
y
X
0 1 2 3 4 5 6 7 8 9 10
10
987654321
Answers
Answer:
y = 2x
Step-by-step explanation:
The graph is of a straight line through the origin. Its slope can be determined from the grid points it passes through. That slope will be the constant of proportionality for the proportion represented.
__
When the graph is a line through the origin, it is a representation of a proportion that can have the equation ...
y = kx
where k is the constant of proportionality, also the slope of the line.
The value of k will be the y-value when x=1. Reading from the graph, we find the line goes through point (1, 2), so y = 2 when x = 1. That means k = 2 and the equation of the line is ...
y = 2x
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction
Submitted
Answers
By using exponent properties, we will get the simplified expression:
[tex]x^{-1}*y^{1/2}*z^2[/tex]
How to simplify the given expression?
Here we have the expression:
[tex](x^{1/2}*y^{-1/4}*z)^{-2}[/tex]
Remember the exponent properties:
[tex](a^n)^m = a^{n*m}[/tex]
And:
[tex](a*b)^n = (a^n)*(b^n)[/tex]
So using these two properties, we can rewrite:
[tex](x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2[/tex]
So we conclude that the completely simplified expression is:
[tex]x^{-1}*y^{1/2}*z^2[/tex]
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Answer:
C
Step-by-step explanation:
Distribute the -2 to the exponents of x, y, and z.
x: 1/2 * -2/1 = -2/2 = -1
y: -1/4 * -2/1 = 2/4 = 1/2
z: 1/1 * -2/1 = -2/1 = -2
Now to get a negative out of the exponents, you simply move them on the other side of the equation (If it is on top move, it to the bottom and vice versa.)
So, once you move all of the exponents you get C.
Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).
Answers
Step-by-step explanation:
Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]
=(2+8/2);(3+9/2)
Midpoint= (5, 6)
Step-by-step explanation:
9. A box contains 50 discs which are numbered 1 to 50. If one disc is drawn at random from the box. Find the probability that it bears: a 2 digit no. (ii) a perfect square no. (iii) a no. divisible by 5
Answers
The probability that it bears a 2 digit no. is 41/50; a perfect square no is; 3/25; a no. divisible by 5 is; 0.2
How to find the probability?
We are given;
Number of Discs in box = 50
Type of discs in box = Numbered 1 to 50
i) Number of 2 digit numbers = 41
Thus;
P(2 digit numbers) = 41/50
ii) Perfect square numbers are; 4, 9, 16, 25, 36 and 49. Thus;
P(perfect square number) = 6/50 = 3/25
iii) Numbers divisible by 5 are; 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Thus;
P(numbers divisible by 5) = 10/50 = 0.2
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Please help me!!!! I would really appreciate it!!!
Answers
Answer:
x=-(7 [tex]\pm i\sqrt(7)[/tex])
Step-by-step explanation:
please help me ASAP
Answers
Answer:
c; 6
Step-by-step explanation:
to find the rate of change from x = 2 to x = 4 you use the (y2 - y1) / (x2 - x1) formula
so
(21 - 9) / (4 - 2)
12 / 2
6
the average rate of change is 6
Express in simplest radical form.
5x√192x³+√3x5
please help!!
Answers
[tex]-5x\sqrt{192x^3} + \sqrt{3x^5}\\\\=-5x\left(192x^3 \right)^{\tfrac 12} + \left(3x^5 \right)^{\tfrac 12}\\\\=-5\cdot (192)^{\tfrac 12} \cdot x \cdot x^{\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\left( 64 \cdot 3 \right)^{\tfrac 12} \cdot x^{1+\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\cdot 8\cdot 3^{\tfrac 12} \cdot x^{\tfrac 15} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-40\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}+3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\[/tex]
[tex]=-39\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-39\sqrt 3 \sqrt{x^5}[/tex]
What is the slope of the line that passes through the points (-6, 8) and (-9, 7)? Write your answer in simplest form.
Answers
Answer:
m=1/3
equation y=1/3x+10
Step-by-step explanation:
Find the rise and run.
1. -6--9=run=3
2. 8-7=rise=1
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)
[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]
y2 & y1 = the y-coordinates of the two points
x2 & x1 = the x-coordinates of the two points
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]
So we substitute the values and obtain:
[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]
Simplifying:
[tex]\bf{\cfrac{-1}{-9+6}}[/tex]
Simplifying more:
[tex]\bf{\cfrac{-1}{-3}}[/tex]
Divide the top and bottom by -1:
[tex]\bf{\cfrac{1}{3}}[/tex]
There's the slope.
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students
What compass heading represents 20° north of west? PLS HELP
Answers
Answer:
West North West
Step-by-step explanation:
West North West would be the bottom half of North West after you split the compass heading into 2 again.
Answer:
north of west = 290 degrees
north of east = 70
Step-by-step explanation:
5/8 of a number is 200. What is 7/10 of the number ?
Answers
Answer:
224Step-by-step explanation:
Let x be the unknown number.
(5÷8)x = 200
Then
x = (8×200) ÷ 5
= 1600 ÷ 5
=320
……………………………
(7/10)x = (7/10)×320
= (7×320) ÷ 10
= 224
Answer:
= 224
Step-by-step explanation:
Hi there!, here is how we solve the problem;
To begin, the question wants us to determine
[tex] \frac{7}{10} [/tex]
of the number x (unknown).
[tex] \frac{5}{8} = 200 \\ \frac{8}{8} = x \\ ( \frac{ \frac{8}{8} \times 200 }{ \frac{5}{8} } ) \\ = \frac{8}{8} \times 200 \times \frac{8}{5} \\ = 320 \\ x = 320[/tex]
We have found our x = 320
Lets now determine
[tex] \frac{7}{10} [/tex]
Which is given by;
[tex]( \frac{7}{10} \times 320 \\ = 224[/tex]
[tex] \frac{7}{10} [/tex]
of the number is therefore 224.
= 224 <<<<<< Ans
I hope this helps.
Have a nice studies.
Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?
A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.
Answers
The equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".
How to write and solve equation?Tina's age = tCole's age = t - 3Cole's age = 18Equate Cole's age
t - 3 = 18
add 3 to both sidest = 18 + 3
t = 21
Therefore, the equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".
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A bicyclist pedals 40 miles in 3 hours. Write the bicyclist's speed as a rate (but not a unit rate yet). Then use the dropdown menus to report the bicyclist's rate. Numerator (top of the fraction): [ Select ] [ Select ] Denominator (bottom of the fraction): [ Select ] [ Select ]
Answers
The bicyclist's speed as a rate is 40/3 miles per hour
How to determine the bicyclist's speed as a rate?The given parameters are:
Distance = 40 milesTime = 3 hoursThe rate is calculated as:
Rate = Distance/Time
Substitute known values
Rate = 40 miles/3 hours
Rewrite as:
Rate = 40/3 miles per hour
Hence, the bicyclist's speed as a rate is 40/3 miles per hour
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Help and please show work!
Factor sin^8Θ + 2sin^4Θcos^4Θ + cos^8Θ
Answers
hi
Step-by-step explanation:
I
don't
know
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