-9x + 12x + 10 simplifies to
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
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
Answer:
a(t)=10000+1.08t
Step-by-step explanation:
t
1
2
3
Alt)
10,800.00
11,664.00
12,597.12
The size of the largest angle in a triangle is 3 times the size of the smallest angle.
The other angle is 35 more than the smallest angle.
Work out in degrees the size of each angle in the trianlge
You must show your working
Answer:
a = 29
b = 64
c = 87
Step-by-step explanation:
Let the angles be a (smallest), b, and c (largest).
We know that a triangle's angles must add up to 180 degrees, so we can construct the following equations.
a + b + c = 180
c = 3a
b = a +35
With some solving and substitution...
a + (a + 35) + c = 180
2a + c = 145
2a + (3a) = 145
5a = 145
a = 29
and therefore,
b = 29 + 35 = 64
c = 3(29) = 87
Answer:
Let smallest angle be :x
So, the largest angle will be:3x
And the other angle will be :x+35
According to angle sum property of triangle,
x+3x+x+35=180
5x+35=180
5x=180-35
5x=145
x=(145/5)
Therefore, x=29
So, the smallest angle =x=29
The largest angle=3x=87
And the other angle=x+35=64
A lottery claims that 3% of tickets win a prize. what is the probability that you win a prize if you purchase twenty tickets?
Factoring Completely:
x^2-16x+48
Answer:
(x - 12)(x - 4)
Step-by-step explanation:
Given
x² - 16x + 48
Consider the factors of the constant term (+ 48) which sum to give the coefficient of the x- term (- 16)
The factors are - 12 and - 4, since
- 12 × - 4 = + 48 and - 12 - 4 = - 16 , thus
x² - 16x + 48 = (x - 12)(x - 4) ← in factored form
Suki typed 245 words in 3
minutes. What is Suki’s typing rate
can someone also give me how to show my work
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.
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)
Answer:
all of the expressions are probably random so I have no idea
6-x=5x+30 know the answer?
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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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
3x + 6y =3 x - y = -7 Does the system have: no solutions, infinite solutions, or one solution?
Answer:
Step-by-step explanation:
3x + 6y = 3
x - y = -7
3x + 6y = 3
-3x - 3y = 21
3y = 24
y = 8
x - 8 = -7
x = 1
(1, 8)
answer is one solution
A box contains nine cards labeled J ,K ,L ,M ,N ,O ,P ,Q , and R. One card will be randomly chosen. What is the probability of choosing a letter from M to P?
Answer:
I think the answer is O
What is the sum of 12 1/4 and it’s additive inverse?
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 .
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.
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.
(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
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].
Round 9.492 to the nearest tenth.
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.
Thirty six divided by 9000 long division
Answer:
9000/6=1500
and
6/9000=0.00067
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
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
Can anyone good with math please help..
Answer:
b
Step-by-step explanation:
lamaoamapa9meudvudjege
U is the midpoint of TV. If TU = x - 6 and TV = 3x – 23, what is TU?
Answer:
TU = 5
Step-by-step explanation:
Since, U is the midpoint of TV.
[tex]\therefore TV = 2 \times TU \\ 3x - 23 = 2(x - 6) \\ 3x - 23 = 2x - 12 \\ 3x - 2x = 23 - 12 \\ x = 11 \\ \\ TU = x - 6 \\ TU = 11 - 6 \\ \huge \red { \boxed{TU = 5}}[/tex]
Simplify:
6(1 + 6x) <6(1 - 5x)
Answer:
x < 0
Step-by-step explanation:
could someone help me with this, I have a few minds left. thanks!! Also marking as brainiest.
Multiply and simplify:
(2x + 8)
A)
2x2 +64
B)
4x? + 64
C)
4x2 + 32x + 64
D)
4x2 + 16x + 16
Answer:
A. 2x+8
Step-by-step explanation:
you take the two and multiply it to the X and the eight and that would give you 2X2 + 64
which angels are corresponding angles check all that apply
C.D.And E..
I'm sure..
If this answer helps you plz mark as brainlist..TqFind m2ABC.
(3x - 70)
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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El productor del números es 28. Sabiendo que el primer número es 3 unidades menor que el segundo, calcula los dos número
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:
Simplify the expression above
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
How many pennies would be in a tower that is 10 miles
high?
median of 2.5, 2.3, 2.3, 1.8, 2.3, 1.5 please help its due today ;(
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
A donut shop made 12 dozen donuts to give to a school’s math club.
Which expression represents how many donuts each student would get if the donuts were equally distributed and there were x
x
students in math club’s
Answer:
Number of donuts each student get = 144 / x
Step-by-step explanation:
Given:
Number of donuts = 12 dozen
Number of students = x
Find:
How many donuts each student get
Computation:
Total number of donuts = 12 × 12 = 144
Number of donuts each student get = Total number of donuts / Number of students
Number of donuts each student get = 144 / x
Pls help Plz help PLZ help
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