Answers
Answer:
top question is the 4th choice.
Step-by-step explanation:
Related Questions
-9x + 12x + 10 simplifies to
Answers
Answer:
[tex] \boxed{\sf 3x + 10} [/tex]
Step-by-step explanation:
Simplify the following:
⇒-9 x + 12 x + 10
Grouping like terms:
⇒(12 x - 9 x) + 10
12 x - 9 x = 3 x:
⇒3 x + 10
(i)Express 2x² – 4x + 1 in the form a(x+ b)² + c and hence state the coordinates of the minimum point, A, on the curve y= 2x² 4x+ 1.
The line x– y + 4 = 0 intersects the curve y= 2x² – 4x + 1 at points P and Q. It is given that the coordinates of Pare (3,7).
(ii)Find the coordinates of
(iii) Find the equation of the line joining Q to the mid-point of AP.
I already get the (i) but hav no idea with no.(ii) and (iii)
Can anyone help me? Thank you
Answers
Answer:
(i). [tex]y = 2\, x^2 - 4\, x + 1 = 2\, (x - 1)^2 - 1[/tex]. Point [tex]A[/tex] is at [tex](1, \, -1)[/tex].
(ii). Point [tex]Q[/tex] is at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex].
(iii). [tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex] (slope-intercept form) or equivalently [tex]x + 5\, y - 17 = 0[/tex] (standard form.)
Step-by-step explanation:
Coordinates of the ExtremaNote, that when [tex]a(x + b)^2 + c[/tex] is expanded, the expression would become [tex]a\, x^2 + 2\, a\, b\, x + a\, b^2 + c[/tex].
Compare this expression to the original [tex]2\, x^2 - 4\, x + 1[/tex]. In particular, try to match the coefficients of the [tex]x^2[/tex] terms and the [tex]x[/tex] terms, as well as the constant terms.
For the [tex]x^2[/tex] coefficients: [tex]a = 2[/tex].For the [tex]x[/tex] coefficients: [tex]2\, a\, b = - 4[/tex]. Since [tex]a = 2[/tex], solving for [tex]b[/tex] gives [tex]b = -1[/tex].For the constant terms: [tex]a \, b^2 + c = 1[/tex]. Since [tex]a = 2[/tex] and [tex]b = -1[/tex], solving for [tex]c[/tex] gives [tex]c =-1[/tex].Hence, the original expression for the parabola is equivalent to [tex]y = 2\, (x - 1)^2 - 1[/tex].
For a parabola in the vertex form [tex]y = a\, (x + b)^2 + c[/tex], the vertex (which, depending on [tex]a[/tex], can either be a minimum or a maximum,) would be [tex](-b,\, c)[/tex]. For this parabola, that point would be [tex](1,\, -1)[/tex].
Coordinates of the Two IntersectionsAssume [tex](m,\, n)[/tex] is an intersection of the graphs of the two functions [tex]y = 2\, x^2- 4\, x + 1[/tex] and [tex]x -y + 4 = 0[/tex]. Setting [tex]x[/tex] to [tex]m[/tex], and [tex]y[/tex] to [tex]n[/tex] should make sure that both equations still hold. That is:
[tex]\displaystyle \left\lbrace \begin{aligned}& n = 2\, m^2 - 4\, m + 1 \\ & m - n + 4 = 0\end{aligned}\right.[/tex].
Take the sum of these two equations to eliminate the variable [tex]n[/tex]:
[tex]n + (m - n + 4) = 2\, m^2 - 4\, m + 1[/tex].
Simplify and solve for [tex]m[/tex]:
[tex]2\, m^2 - 5\, m -3 = 0[/tex].
[tex](2\, m + 1)\, (m - 3) = 0[/tex].
There are two possible solutions: [tex]m = -1/2[/tex] and [tex]m = 3[/tex]. For each possible [tex]m[/tex], substitute back to either of the two equations to find the value of [tex]n[/tex].
[tex]\displaystyle m = -\frac{1}{2}[/tex] corresponds to [tex]n = \displaystyle \frac{7}{2}[/tex]. [tex]m = 3[/tex] corresponds to [tex]n = 7[/tex].Hence, the two intersections are at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] and [tex](3,\, 7)[/tex], respectively.
Line Joining Point Q and the Midpoint of Segment APThe coordinates of point [tex]A[/tex] and point [tex]P[/tex] each have two components.
For point [tex]A[/tex], the [tex]x[/tex]-component is [tex]1[/tex] while the [tex]y[/tex]-component is [tex](-1)[/tex].For point [tex]P[/tex], the [tex]x[/tex]-component is [tex]3[/tex] while the [tex]y[/tex]-component is [tex]7[/tex].Let [tex]M[/tex] denote the midpoint of segment [tex]AP[/tex]. The [tex]x[/tex]-component of point [tex]M[/tex] would be [tex](1 + 3) / 2 = 2[/tex], the average of the [tex]x[/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].
Similarly, the [tex]y[/tex]-component of point [tex]M[/tex] would be [tex]((-1) + 7) / 2 = 3[/tex], the average of the [tex]y\![/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].
Hence, the midpoint of segment [tex]AP[/tex] would be at [tex](2,\, 3)[/tex].
The slope of the line joining [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] (the coordinates of point [tex]Q[/tex]) and [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) would be:
[tex]\displaystyle \frac{\text{Change in $y$}}{\text{Change in $x$}} = \frac{3 - (7/2)}{2 - (-1/2)} = \frac{1}{5}[/tex].
Point [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) is a point on that line. The point-slope form of this line would be:
[tex]\displaystyle \left( y - \frac{7}{2}\right) = \frac{1}{5}\, \left(x - \frac{1}{2} \right)[/tex].
Rearrange to obtain the slope-intercept form, as well as the standard form of this line:
[tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex].
[tex]x + 5\, y - 17 = 0[/tex].
Suki typed 245 words in 3
minutes. What is Suki’s typing rate
can someone also give me how to show my work
Answers
Answer:
81 2/3 words per minute
Step-by-step explanation:
245/3= 81 2/3
Answer:
Suki's typing rate is 82wpm
Step-by-step explanation:
Words per minute is a typing rate calculated by the minutes that the person has typed for and the amount of words that they typed. In this case I did 245 / 3 which is 81.6666666667 , but words per minute has to be round up to the nearest number, so if it were 81 to 81.49 it would go to 81, if it were 81.5 to 81.99 it would go to 82. So since it is 81.6 it goes up to 82wpm.
Work out the direction of the resultant force on the object. Define the horizontal axis as
the origin of angle and turn clockwise as positive. Give the answer in degrees to 2 sig.
20 points! will mark brainliest
fig.
Answers
Answer:
53°
Step-by-step explanation:
If you translate the 4 N force to the right so its tail is at the tip of the 3 N force, you see these are the legs of a 3-4-5 right triangle. The 4 N force is opposite the angle of interest, and the 3 N force is adjacent. Then the angle of interest, α, has the relation ...
Tan = Opposite/Adjacent
tan(α) = 4/3
α = arctan(4/3) ≈ 53°
The direction of the resultant is 53° clockwise from the horizontal axis.
Can anyone good with math please help..
Answers
Answer:
b
Step-by-step explanation:
lamaoamapa9meudvudjege
Find m2ABC.
(3x - 70)
Answers
Answer:
Step-by-step explanation:
3x - 70 = x
2x = 70
x = 35
3(35) - 70
105 - 70 = 35
m<ABC = 35
answer is C
The value of the angle ∠ABC = 35°
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the angle be ∠ABC = ( 3x - 70 )°
Now , from the figure ,
The value of angle ∠A = x°
The value of x° is equal to ( 3x - 70 )° because they are corresponding angles
Now , from the theorem of angles cut by transversal , we get
The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size
Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other
So ,
Substituting the values in the equation , we get
x° is equal to ( 3x - 70 )°
x° = ( 3x - 70 )°
x = 3x - 70
Adding 70 on both sides of the equation , we get
3x = x + 70
Subtracting x on both sides of the equation , we get
2x = 70
Divide by 2 on both sides of the equation , we get
x = 35°
So , the value of ∠ABC = ( 3x - 70 )°
∠ABC = ( 3x - 70 )°
∠ABC = ( 135 - 70 )°
∠ABC = 35°
Hence , The value of the angle ∠ABC = 35°
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Simplify the following expression by combining like terms 5x^2 + 6x - 3 + 4x^2 + - 8x +2
Answers
I Need help asap. PLZ
Answers
Answer:
x = 12
Step-by-step explanation:
The 2 given angles are same- side interior angles and are supplementary, thus
9x - 4 + 5x + 16 = 180, that is
14x + 12 = 180 ( subtract 12 from both sides )
14x = 168 ( divide both sides by 14 )
x = 12
6-x=5x+30 know the answer?
Answers
Answer:x=-4
Step-by-step explanation:
move 5x to the other side by cancelling it out with -5x
that causes it to be 6-6x=30
move 6 to other side by cancelling out with -6
causes it to be -6x=24
divide by -6 to get x alone
x=24/-6
answer is -4 when reduced
The solution to the equation 6 - x = 5x + 30 is x = -4.
To solve the equation 6 - x = 5x + 30, follow these steps:
Start by combining like terms on each side of the equation:
6 - x = 5x + 30
Rearranging the equation:
6 - 30 = 5x + x
-24 = 6x
Divide both sides of the equation by 6 to isolate the variable x:
-24/6 = 6x/6
-4 = x
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Pls help Plz help PLZ help
Answers
Answer:
Step-by-step explanation:
E=9x-38
F=2x+40
9x+2x+2=90
11x=90-2
11x=88
x=88/11=8
F=2*8+40
16+40
=56
Simplify the expression above
Answers
Answer:
2x²
Step-by-step explanation:
Answer:
11y-5
Step by step:
X^2-8x^2+7x^2=0
x+x-2x=0
3-8=-5
2y+9y=11y
Oranges are on sale for a $1.59 per pound write a function as a standard equation
Answers
What is the sum of 12 1/4 and it’s additive inverse?
Answers
Given :
A number [tex]12\dfrac{1}{4}=\dfrac{49}{4}[/tex] .
To Find :
What is the sum of 12 1/4 and it’s additive inverse .
Solution :
Fist we should know what is additive inverse .
Additive inverse of a number is that number , when added to it yield zero ,
Basically , for a real number , it reverses its sign :
The opposite to a positive is negative .
The opposite to a negative is positive .
Therefore , the sum of [tex]12\dfrac{1}{4}[/tex] and it's additive inverse is 0 .
Hence , this is the required solution .
A child's ladder is made of 3 sections. Each section is 3/4 meters. How long is the ladder when all 3 sections are extended to make
one ladder?
O A. 1 meter
.
B. 9/4 meters
O C. 1414 meters
OD. 3/2 meters
Answers
Answer:
2 1/4
Step-by-step explanation:
Because I got it wrong and it showed me the answer. YOUR WELCOME
Answer:
2 1/4
Step-by-step explanation:
got it corrrect
Which expressions are equivalent to x4 + 5x3 - 43x2 + 4x -9? Select all that apply. (-6x4 - 8x3 - 34x2 + 4x - 23) + (7x4 + 13x3 – 9x2 + 14) A B (x4 + 2x3 - 203x2 + 9x – 13) + (x4 + 3x3 + 160x2–5x + 4) C (3x4 + 1983 - 7x2 + x - 193) - (2x4 + 14x3 + 36x2 – 3x – 184) (13x4 - 11x3 + 8x2 + 5x – 19) - (-12x4 + 16x3 - 51x2 - x + 10) (-8x4 - 31x3 – 11x2 - 8x - 43) - (-9x4 + 36x3 – 32x2 + 12x + 34)
Answers
Answer:
all of the expressions are probably random so I have no idea
How many pennies would be in a tower that is 10 miles
high?
Answers
a mile high) of a penny, then divide 5280 feet by whatever you find.
This is a great activity for a class, and in fact a good way to start
the project. First take one penny, and work out an answer. Then get
100 pennies, and measure them; do the same calculation to see how many
pennies it will take to make a mile. There will probably be a
difference, because you can measure 100 pennies more accurately than a
single penny. Or maybe you have a micrometer that will measure one
penny precisely. Which is better can be a good discussion starter. And
don't forget to try it in metric, too.
Just to illustrate, using a very rough estimate of a penny's width,
let's say a penny is about 3/4 inch wide. The number of pennies in a
mile will be
5280 ft 12 in 1 penny
1 mile * ------- * ----- * ------- = 5280 * 12 * 4/3 pennies
1 mi 1 ft 3/4 in
This gives about 84,480 pennies. (This method of doing calculations
with units is very helpful, and would be worth teaching.)
If we measure 100 pennies as 6 ft 1 in, we will get
5280 ft 100 pennies
1 mile * ------- * ----------- = 5280 * 100 * 12 / 73 pennies
1 mi 6 1/12 ft
This gives us 86794.5205 pennies in a mile.
What would be the actual length, if the length of the model is 25 ft and the scale factor is less
than one?
20 ft, 25 ft, Or 30 ft
Answers
Answer:
20ft
Explanation:
You multiply the model length by the scale factor to find the actual length. If the scale factor is less than zero, then the actual size will be smaller than the model. Therefore, your answer would be 20ft.
Specifically, the scale factor is .8 if the actual size is 20ft, 1 if the actual size is 25ft, and 1.2 if the actual size is 30ft.
The actual length of the model will be 30 feet. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The length of the model is 25 feet. And the scale factor is less than one.
We know that if the scale factor is from zero to one, then the size of the actual length increases.
If the scale factor is greater than zero, then the size of the actual length decrease.
And if the scale factor is one, then the size does not change.
The size of the actual length will be greater than 25 feet.
The actual length of the model will be 30 feet. Then the correct option is C.
More about the dilation link is given below.
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What is the slope of the line on the graph?
Answers
Answer:
2/4=1/2
Step-by-step explanation:
It rises 2 runs over 4.
rise/run
2/4=1/2
which angels are corresponding angles check all that apply
Answers
C.D.And E..
I'm sure..
If this answer helps you plz mark as brainlist..TqThirty six divided by 9000 long division
Answers
Answer:
9000/6=1500
and
6/9000=0.00067
If it is 9 AM, what time was it 57 hours ago.
Answers
Answer:
1. am
Step-by-step explanation:
work is shown and pit
El productor del números es 28. Sabiendo que el primer número es 3 unidades menor que el segundo, calcula los dos número
Answers
Answer:
Tienes 3 números, "x", "y", "z"
=> El primero es 20 unidades menor que el segundo:
El primero es "x", y el segundo es "y", entonces:
x = y - 20
=> El tercero es igual a la suma de los dos primeros:
El tercero es "z", entonces:
z = x + y
z = (y - 20) + y
z = 2y - 20
=> Entre los tres suman 120
x + y + z = 120
y - 20 + y + 2y - 20 = 120
4y - 40 = 120
4y = 160
y = 40
Si y = 40, entonces:
x = y - 20
x = 20
Además, z = 2y - 20
z= 60
RPTA:
x=20
y=40
z=60
Step-by-step explanation:
could someone help me with this, I have a few minds left. thanks!! Also marking as brainiest.
Answers
so √10 is located between √9 and √16
A lottery claims that 3% of tickets win a prize. what is the probability that you win a prize if you purchase twenty tickets?
Answers
=3% X 20
=3/100 X 20
=60/100
=6/10
=0.6
Ans: The probability of winning a prize if we purchase 20 tickets is 0.6
(-2)(8)(-6) divided-4
Answers
Answer: -24
Step-by-step explanation:
-2 * 8 = -16
-16 * -6 = 96
Answer:
24 Please give brainliest
Step-by-step explanation:
-2 x 8
-16 x -6
96/4
24
3. A $1,250 deposit for 10 years at a simple interest rate of 5.25%
Answers
Step-by-step explanation:
I=(pxRxt)/100
I=(1250×5.25×10)/100
I=656.25
amount to be paid is $1906.25 pls give me brainliest
A company invests $10,000 in a mutual fund account that earns a fixed
interest per year. The account balance, Alt), in dollars, after t years is shown
in the table below.
t
1
2
3
Alt)
10,800.00
11,664.00
12,597.12
Which of the following equations represents Aſt)?
A(t) = 10,000 + 1.08t
A(t) = 10,000(1.08) - 1
A(t) = 10,800(1.08)
A(t) = 10,800(1.08) - 1
You
Answers
Answer:
a(t)=10000+1.08t
Step-by-step explanation:
t
1
2
3
Alt)
10,800.00
11,664.00
12,597.12
Enrico translates figure Q to get figure Q’. Then he rotates figure Q’ to get figure Q’. Explain why figure Q and figure Q’’ are congruent
Answers
Round 9.492 to the nearest tenth.
Answers
Answer:
9.5
Step-by-step explanation:
The correct answer is 9.5 because 9.49 is closer to 9.5 than 9.4
Answer:
9.5
Step-by-step explanation:
9.492 to the nearest tenth
First you would round 0.092, which would just be 0.09 because 2 is less than 5. You would then have 9.49. You would then round the 0.49, and since 9 is greater than 5, it would be 9.5 because 9 would round to 10.
median of 2.5, 2.3, 2.3, 1.8, 2.3, 1.5 please help its due today ;(
Answers
Answer:
I got 2.3
Step-by-step explanation:
line them up in order and count from the outside
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2.3}}}}}[/tex]
Step-by-step explanation:
[tex] \star{ \tt{ \: Given \: data}}[/tex] :
[tex] \sf{2.5 \: , \: 2.3 \: , \: 2.3 \: , \: 1.8 \: , \: 2.3 \: , \: 1.5}[/tex]
[tex] \star{ \sf{ \: Arranging \: the \: given \: data \: in \: ascending \: order}}[/tex] :
[tex] \sf{1.5 \: , \: 1.8 \: , \: 2.3 \: , \: 2.3 \: , \: 2.3 \: , \: 2.5}[/tex]
[tex] \star{ \sf{ \: n \: ( \: Total \: number \: of \: observation \: ) \: = \: 6}}[/tex]
Finding the position of median
[tex] \bold{ \boxed{ \sf{ \: Position \: of \: median = ( \frac{n + 1}{2} ) ^{th} item}}}[/tex]
[tex] \longmapsto{ \sf{position \: of \: median = ( \frac{6 + 1}{2} ) ^{th} item}}[/tex]
[tex] \longmapsto{ \sf{position \: of \: median \: = \: ( \frac{7}{2} ) ^{th} item}}[/tex]
[tex] \longmapsto {\sf{position \: of \: median = {3.5}^{th} item}}[/tex]
[tex] \sf{ {3.5}^{th} }[/tex] item is the average of 3rd and 4th items.
[tex] \sf{∴Median = \frac{ {3}^{rd} item + {4}^{th} item}{2} }[/tex]
[tex] \longmapsto{ \sf{median = \frac{2.3 + 2.3}{2}}} [/tex]
[tex] \longmapsto{ \sf{median = \frac{4.6}{2} }}[/tex]
[tex] \longmapsto{ \sf{median = 2.3}}[/tex]
∴ Median = 2.3
-------------------------------------------------------------
[tex] \star \: \underline{ \tt{Remember ! }}[/tex]
▪️If n is odd , the median is the value of the [tex] \sf{( \frac{n + 1}{2} ) ^{th} }[/tex] observation.
▪️If n is even, the median is the average of [tex] \sf{( \frac{n}{2} ) ^{th}} [/tex] and [tex] \sf{( \frac{n}{2} + 1) ^{th} }[/tex] observation.
Hope I helped!
Best regards! :D
~TheAnimeGirl