[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]
Factor the expression with the common factor that is "a²".[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]
MissSpanishAnswer:
a²(a²-a+2)
Step-by-step explanation:
Solution Given:
a⁴-a³+2a²
first taking common a²
we get
a²(a²-a+2) which is a required answer.
PLEASE HURRY WILL GIVE POINTS AND BRAINLYEST TO FIRST RIGHT!!!
Answer:
(0, 4) and (-1, 0)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=2x^2+6x+4\\y=-4x^2+4\end{cases}[/tex]
Solve by substitution
Substitute the first equation into the second:
[tex]\implies 2x^2+6x+4=-4x^2+4[/tex]
Add 4x² to both sides:
[tex]\implies 2x^2+6x+4+4x^2=-4x^2+4+4x^2[/tex]
[tex]\implies 6x^2+6x+4=4[/tex]
Subtract 4 from both sides:
[tex]\implies 6x^2+6x+4-4=4-4[/tex]
[tex]\implies 6x^2+6x=0[/tex]
Factor out 6x from the left side:
[tex]\implies 6x(x+1)=0[/tex]
Therefore:
[tex]\implies 6x=0 \implies x=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
To find the y-coordinates of the found x-values, substitute the found values of x into one of the equations:
[tex]x=0 \implies -4(0)^2+4=4 \implies (0,4)[/tex]
[tex]x=-1\implies -4(-1)^2+4=0\implies (-1,0)[/tex]
Therefore, the solutions to the system of equations are:
(0, 4) and (-1, 0)
Answer:
Solutions:
a) x = 0, y = 4 ⇒ (0, 4)
b) x = -1, y = 0 ⇒ (-1, 0)
Step-by-step explanation:
Given system of equations:
a) y = 2x² + 6x + 4
b) y = -4x² + 4
1. Substitute the value of y in the second equation into the first equation:
⇒ -4x² + 4 = 2x² + 6x + 4
2. Solve for x:
⇒ -4x² + 4 = 2x² + 6x + 4 [subtract 4 from both sides]
⇒ -4x² + 4 - 4 = 2x² + 6x + 4 - 4
⇒ -4x² = 2x² + 6x [subtract 2x² from both sides]
⇒ -4x² - 2x² = 2x² - 2x² + 6x
⇒ -6x² = 6x [subtract 6x from both sides]
⇒ -6x² - 6x = 6x - 6x
⇒ -6x² - 6x = 0 [factor out -6x from the equation]
⇒ -6x(x + 1) = 0
Two cases:
a)
⇒ -6x = 0 [divide both sides by -6]
⇒ -6x ÷ -6 = 0 ÷ -6
⇒ x = 0
b)
⇒ x + 1 = 0 [subtract 1 from both sides]
⇒ x + 1 - 1 = 0 - 1
⇒ x = -1
3. Find the value of y by substituting the found x values into one of the given equations:
a) x = 0:
⇒ y = -4x² + 4
⇒ y = -4(0)² + 4
⇒ y = -4(0) + 4
⇒ y = = 0 + 4
⇒ y = 4
coordinate: (0, 4)
b) x = -1:
⇒ y = -4x² + 4
⇒ y = -4(-1)² + 4
⇒ y = -4(1) + 4
⇒ y = -4 + 4
⇒ y = 0
coordinate: (-1, 0)
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which expression is in simplest form?
Answer:
A.
Step-by-step explanation:
let me know if you want an explanation :))
Find the accumulated amount of an account if the principal amount was 5000 at 16% interest at the end of 3 years
Answer:
2400
Step-by-step explanation:
Find the accumulated amount of an account if the principal amount was 5000 at 16% interest at the end of 3 years
Solution
The formula for simple interest
S.I = P *R* T/100
Where P = Principal = 5000
R = Rate = 16%
T = Time = 3 years
5000 * 16 * 3/100
50 * 16 * 3
= 2400.
There are 7 pieces of pie left over in the cafeteria l. If 5 pieces are apples and 2 are cherry, what fraction of the remaining pieces are cherry?
Answer:
2/7
Step-by-step explanation:
To find the fraction that are cherry, take the number that are cherry and put that over the total number of pieces
2 cherry
----------------
7 total
The fraction that are cherry are 2/7
1. What are you going to make? (6 points) (Note: The maximum
build size is 25 cm by 16 cm by 15 cm - about the size of a small
shoe box.)
Answer: You have already given the answer in the question! You can make a small shoe box.
the sum of the 10th and 11th terms of an arithmetic sequence is 65 what is the sum of its first 20th terms
Answer:
this is the answer
Step-by-step explanation:
a 65
b 650
c 52
d 3
Use the drawing tools to sketch the graph of a rational function with a domain of { x | x ∈ R , x ≠ - 5 , 4 } . Include one removable discontinuity and one nonremovable discontinuity. Label each discontinuity using the text tool.
If [tex]f(x)[/tex] has a removable discontinuity at [tex]x=a[/tex], then the limit
[tex]\displaystyle \lim_{x\to a} \frac{f(x)}{x-a}[/tex]
exists and is finite.
A non-removable discontinuity at [tex]x=b[/tex] would entail a non-finite limit,
[tex]\displaystyle \lim_{x\to b} \frac{f(x)}{x-b} = \pm\infty[/tex]
or the limit does not exist (which could be due to the limits from either side of [tex]x=b[/tex] not matching or existing).
For a rational function, we want
[tex]f(x) = \dfrac{p(x)}{q(x)}[/tex]
where [tex]p[/tex] and [tex]q[/tex] are polynomials in [tex]x[/tex]. To get a removable discontinuity at [tex]x=a[/tex], both [tex]p[/tex] and [tex]q[/tex] must be divisible by [tex]x-a[/tex], and the limit of their quotient after removing these factors still exists. That is,
[tex]\displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \frac{p(x)}{q(x)} = \lim_{x\to a} \frac{(x-a)p^*(x)}{(x-a)q^*(x)} = \lim_{x\to a} \frac{p^*(x)}{q^*(x)} = \frac{p^*(a)}{q^*(a)}[/tex]
On the flip side, we get a non-removable discontinuity [tex]x=b[/tex] if [tex]p[/tex] is not divisible by [tex]x-b[/tex], in which case
[tex]\displaystyle \lim_{x\to b} f(x) = \lim_{x\to b} \frac{p(x)}{q(x)} = \lim_{x\to b} \frac{p(x)}{(x-b)q^*(x)} = \frac{p(b)}{0\times q^*(b)}[/tex]
and this is undefined.
Suppose [tex]f(x)[/tex] has a non-removable discontinuity at [tex]x=-5[/tex] and a removable one at [tex]x=4[/tex]. Then one such function could be
[tex]f(x) = \dfrac{x-4}{(x-4)(x+5)} = \dfrac{x-4}{x^2+x-20}[/tex]
Is this pattern a net for the three-dimensional figure?
no
yes
Answer:
no
Step-by-step explanation:
the bet displays 3 hexagonal bases when in the figure there is only 2 bases.
Answer:
No.
Step-by-step explanation:
Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.
A cylinder has a diameter of 14 cm and height of 20cm . find the curved surface area
Answer:
879.6452 cm
Step-by-step explanation:
The curved surface area of a cylinder is calculated using the formula, curved surface area of cylinder = 2πrh, where 'r' is the radius and 'h' is the height of the cylinder.
diameter = 2r
14=2(r)
7=r
2(π)(7)(20) cm
2(3.14159)(7)(20)
879.6452
Someone help me with this math word questions
2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.
3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]
4) [tex]X[/tex]
Lewis has a net spendable income of $2,000 per month. He sets up the following transportation budget for himself.
3. Transportation (15% - 20%) 400
a. Car payments 210
b. Gas/Oil 120
c. Insurance 60
d. License/Registration 8
e. Taxes 2
f. Maintenance/Repair
What has Lewis done wrong?
What Lewis did wrong was that; He budgeted more than the maximum recommended amount of money for transportation.
How to budget effectively?
We are given;
Net spendable income = $2,000 per month
Now, we see how much he has budgeted for other items such as Car payments, Gas/Oil, Insurance, License/Registration, Taxes, Maintenance/Repair.
Now, from the recommended transportation budget of between 15% - 20% of the net spendable income, we can see that he would likely spend more than that if we add the cost of maintenance and repair.
Thus, what Lewis did wrong was that he budgeted more than the maximum recommended amount of money for transportation.
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Answer:
Step-by-step explanation:
Answer:
A. He budgeted more than the maximum recommended amount of money for transportation. PLATO (Im 100% sure
describe the effect of the transformation (x,y) to (x,y+4)
A. vertical stretch without reflection
B. horizontal translation of 4 units
C. vertical stretch with reflection
D. Vertical translation of 4 units
DF=
Help me please:))
Answer:
[tex]\fbox {DF = 20}[/tex]
Step-by-step explanation:
Given :
ΔSDF ~ ΔRTY = 4 : 9 (Ratio of similitude)SF = RT - 2TY = RY + 9SD = 8Step 1 : Find RT
SD : RT = 4 : 98 : RT = 4 : 9RT = 18Step 2 : Find SF
SF = RT - 2SF = 18 - 2SF = 16Step 3 : Find RY
SF : RY = 4 : 916 : RY = 4 : 9RY = 36Step 4 : Find TY
TY = RY + 9TY = 36 + 9TY = 45Step 5 : Find DF
DF : TY = 4 : 9DF : 45 = 4 : 9DF = 20Answer:
DF = 20
Step-by-step explanation:
Triangle SDF has side lengths SD, DF, SF.
Triangle RTY has side lengths
RT = (9/4)SD
RY = (9/4)SF
TY = (9/4)DF
"SF is 2 less than RT" Given
SF = RT - 2
SF = (9/4)SD - 2
"SD = 8" Given
SF = (9/4)(8) - 2
SF = 16
"TY is 9 more than RY" Given
TY = RY + 9
(9/4)DF = (9/4)SF + 9
(9/4)DF = (9/4)(16) + 9
(9/4)DF = 45
DF = 45 × 4/9
DF = 20
ZY = 34, WY = 38, and m/ZXY = 34° find WZ
The value of the WZ will be 28.18. The given figure is quadrilateral.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D shapes.
In ΔZXY
∠Z+∠X+∠Y=180
∠Z+34°+90°=180°
∠Z = 56°
In Δ WZY
sin Θ = WZ/ZY
sin 56° = WZ/34
WZ= 28.18
Hence, the value of the WZ will be 28.18.
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The side WZ = 30.4.
What are alternate angles?The angles which lie on the alternate side of the line between two parallel lines.
Given a geometry in which ZY = 34, WY = 38, and ∠ZXY = 34°
In this geometry, opposite sides are equal.
WZ = XY and WX = ZY.....................(1)
The diagonal are perpendicular to each other.
∠XVY = 90°
Diagonal form four right angle triangles. Take ΔXVY
VY = WY/2
VY = 38/2
VY = 17
Using trigonometric property,
sin X° = VY / XY
sin 34° = 17/XY
XY = 30.4
From equation 1, we have
WZ = 30.4
Thus, the value of WZ is 30.4.
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If the proportion of the total disposable income spent on consumer goods and services is 93 percent and if
consumers spend 85 percent of each additional dollar, what is
a. the apc?
b. the aps?
c. the mpc?
d. the mps?
Answer:
what?????????????????
its math help me out
Answer:
each one is double the one before it so in year 5...
3912*2=7824
Hope This Helps!!!
Answer:
7824
Step-by-step explanation:
Question 12 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
A. -5
B. 3
C. 2
☐D. O
E. 1
F. -3
5
1 is the values are in the range of the function graphed below. Option E is corect.
What is the difference between domain and range?The domain denotes all potential x values, while the range denotes the domain's possible y values.
The domain is the value of x which lies between the -2 ≤ x ≤ 1.While the range shows the value of y which is equal to 1.
Hence, option E is correct
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A student begins a proof of the law of cosines. His work is shown.
(image below)
The student made an error in ___. To correct this error, he should ___.
After correcting this error, the student can use the ___ to relate sides x, y, z, and angle ___.
1st blank answers:
a, step 1
b, step 2
c, step 3
2nd blank answers
a, define side AY in terms of angle X
b, define side XY in terms of angle X
c, define side AX in terms of angle Y
3rd blank answers
a, tangent function
b, law of sines
c, Pythagorean theorem
4th blank answers
a, Z
b, X
c, Y
The student made an error in step 3. To correct this error, he should define side AY in terms of angle X. Pythagorean theorem relates sides x, y, z, and angle X
The law of cosine.In Trigonometry, law of cosine (cos) is given by this mathematical expression:
cosθ = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this scenario, we can logically deduce that the student made an error in step 3. To correct this error, he should define side AY in terms of angle X.
After correcting this error, the student can use the Pythagorean theorem to relate sides x, y, z, and angle X.
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8 1/2 - 3/8=?
pls answer fast
Answer:
65/8
Step-by-step explanation:
1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?
2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8
3) Can not simplify since there are no common factors between 65 and 8.
please help
Find the sum or type
“impossible”
Answer:
finished this question is from matric it is very easy
HELPP
Simplify the expression 6^3+ 5(4 − 2).
28
36
226
234
Answer:
BODMAS
[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]
Answer: Answer is 226
Step-by-step explanation: Do math
6.11.4 Test(TST): Circles Without Coordinates). The questions are in the document.
The value of AOB and BOC based in the information given in the circle will be 53°.
How to calculate the values in the circle?From the information given, the central angle is the angle that the vertex is at the center of the circle.
It was stated that OB bisects AOC. Therefore, since AOB is 53°, BOC is also 53°.
The value of AOC will now be:
= AOB + BOC
= 53° + 53°
= 106°
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vanessa deposited money into a bank account yhat earned 1.25% simple interest after each year. after 1/2 year she earned $5 in interest on the account. how much was her initial deposit
The initial amount is $800.
What is interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
Given:
Simple interest = 1.25% = 0.0125
So, interest in half a year.
=0.0125 ÷ 2
= 0.00625
Now,
=5 / 0.00625
= 800
Hence, the initial deposit was $800
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Write an equation for each translation of y=|x|
13 units down
y-13= |x|
y=1x1-13
y=1-13x1
y=1x1+13
The answer is y=|x|-13.
Answer:
y=|x|-13
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of:
(-1,7) and (3,-2)
Give coordinates as decimals where appropriate.
Answer:
(1,2.5)
Step-by-step explanation:
On the graph, the (-1,7) lies in the top right grid. The (3,-2) lies in the bottom left grid. If you use a graphing calculator, the middle is hard to find but you will find (1, 2.5) or (1, 5/2).
find the value of x in the given figure
To solve this problem, you will first use the Angle Sum Property to determine the value of x after creating an algebraic equation, combining like terms, and subtracting from both sides of an equation.
Use the Angle Sum PropertyThe Angle Sum Property states that all interior angles of a triangle will summate to 180º.
An equation can be created to find this when you are given two angles and missing a third. That third angle can be referred to as x in this scenario.
Adding the two known angles and the unknown angle will result in a sum of 180º. This means that our unknown is x and can therefore be placed in an equation:
[tex]65+42+x=180[/tex]
Combine Like TermsCombine the like terms by combining the constants on the left side of the equation using addition:
[tex]65+42+x=180[/tex]
[tex]107+x=180[/tex]
SubtractAfter combining like terms, subtract 107 from both sides of the equation:
[tex]107 - 107 +x = 180-107[/tex]
[tex]\boxed{x=73}[/tex]
The final answer is x = 73 degrees.
a. Write an expression for the value of the account at the end of three years in terms of the growth factor x
Express (x-8x)^2 as a trinomial in standard form
Answer:
(x - 8x)²
(x - 8x) (x - 8x).
using the identity
( a - b) ² = a² + b² - 2ab
a = x
b = 8x
x² + 64x - 16x²
find the measure of arc DB in P
please hurry if you can
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:m\overbrace{DB}= 90 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + m \overbrace{TB} = 180 \degree[/tex]
[ linear pair ]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + 90 \degree = 180 \degree[/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 180 \degree - 90 \degree[/tex]
[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 90 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km/hr. At 8.30 am a car left Busia for Nairobi at an average speed of 120km/hr. Given that the distance between Nairobi and Busia is 400km. ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
The time that the bus arrived Busia is given as 1.00 pm
How to solve for the time of arrivalThe formula with which to solve for the time is given as
D/s = distance / by the speed.
Distance = 400km
Speed = 80km/hr
Time = 400/80
= 5 hours
Therefore the time of arrival from 8.00 am would be 1.00pm
Complete questionA bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
Calculate The time the car arrived in Busia
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