Answer:
2x(x^2 - 3)(x^2 + 9)
Step-by-step explanation:
2x^5 + 12x^3 − 54x
2x(x^4 + 6x - 27)
Since -3 + 9 = 6 and -3 x 9 = -27:
2x(x^2 - 3)(x^2 + 9)
Answer:
[tex]2x(x^2-3)(x^2+9)[/tex]
Step-by-step explanation:
Given polynomial:
[tex]2x^5+12x^3-54x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies 2x(x^4+6x^2-27)[/tex]
To factor the trinomial [tex]x^4+6x^2-27[/tex]:
[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]
Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3
Rewrite the middle term as the sum of these two numbers:
[tex]\implies u^2+9u-3u-27[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+9)-3(u+9)[/tex]
Factor out the common term (u + 9):
[tex]\implies (u-3)(u+9)[/tex]
Substitute back [tex]u=x^2[/tex]:
[tex]\implies (x^2-3)(x^2+9)[/tex]
Therefore, the factored form of the given polynomial is:
[tex]\implies 2x(x^2-3)(x^2+9)[/tex]
Victor just bought a new television for $682.00. He made a down payment of $55.00 and will pay monthly payments of $33.00 until it is paid off. How many months will Victor be paying? (Assume that Victor pays no interest.)
Answer:
19 months
Step-by-step explanation:
First off 682- 55 = 627. 627/33 = 19
what is the answer for this question much appreciated if you attempt to help me
Answer:
The surface area of the triangular prism is [tex]624cm^{2}[/tex]
Step-by-step explanation:
First find the area of the triangle.
The formula of the area of triangle is: [tex]\frac{1}{2} * h*b[/tex]
h=height
b=base or width.
[tex]\frac{1}{2}*16*12[/tex]
But, since we have two triangles we can skip the [tex]\frac{1}{2}[/tex] because [tex]2*\frac{1}{2} =1[/tex].
[tex]16*12=192[/tex], that is the area of the two triangles combined.
Now let's find the area of the rectangles. I'll start with the diagonal one.
The formula of the area of the rectangle is: [tex]h*b[/tex].
[tex]20*9=180[/tex].
The next rectangle.
[tex]9*16=144[/tex]
The final rectangle.
[tex]12*9=108[/tex]
Now combine all the areas to find the surface area of the triangular prism.
[tex]192+180+144+108=624[/tex]
The surface area of the triangular prism is [tex]624cm^{2}[/tex]
Hope this helps!
If not, I am sorry.
A line that includes the point (0, 6) has a slope of 1/3. What is its equation in slope-intercept
form?
Answer:
y=⅓x+b
Step-by-step explanation:
So basically the formula of slope-intercept is:
y=mx+b
and m=⅓
so
y=⅓x+b and it includes the point (0, 6) so:
6=⅓(0)+b===> b=6===> y=⅓x+6
choose the system of equations!!
Answer:
It is the FOURTH OPTIONor D
Drag a statement or reason to each box to complete this proof.
If −3(x+8)=−21, then x=−1.
(Please refer to attached image for more info.)
Answer:
1. -3(x+8) = -21
2. Division property of equality
3. x + 8 = 7
4. Subtraction Property of Equality
(Not quite sure whether #2 is division or distributive, but i'm 90% sure it's division).
Venn diagrams in maths
Answer:
Step-by-step explanation:
The slope of the line below is 2. Use the coordinates of the labeled point to
find a point-slope equation of the line.
• (3,10)
) A. y+ 10 = 2(x+ 3)
B. y - 10 = -2(x- 3)
D C. y + 10 = -2(x+3)
D. y - 10 = 2(x - 3)
Answer:
y - 10 = 2(x - 3)
Explanation:
Equation:
y - y₁ = m(x - x₁)
Here given:
coordinates: (x, y) = (3, 10)
x₁ = 3y₁ = 10slope (m) = 2Inserting value's:
y - 10 = 2(x - 3) in point slope form
y = 2x - 6 + 10
y = 2x + 4 in slope-intercept form
Answer:
d) y - 10 = 2(x - 3)
Step-by-step explanation:
Given: a line with a slope of 2, and the point (3, 10)
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
where: m is the slope, and (x₁, y₁) is a given point
Substitute the values into the form:
⇒ y - y₁ = m(x - x₁)
⇒ y - 10 = 2(x - 3)
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pls help with age problem.
Answer:
John is 19 and his sister is 23.
Step-by-step explanation:
See attached image.
What is a name for the marked angle?
Answer:
angle CAD
Step-by-step explanation:
look at the 3 points that make up the angle
PLEASE HELP!!!!!
Estimate the solution to the system of equations.
y=4x−2
y=x+3
(Choice A)
x= 2/3
y= 4 2/3
(Choice B)
x= 1 2/3
y=3 2/3
(Choice C)
x= 1 2/3
y=4 2/3
(Choice D)
x=2/3
y= 3 2/3
The value of the variable x and y will be 1 2/3 and 4 2/3. Then the correct option is C.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
y = 4x − 2 ...1
y = x + 3 ...2
Subtract equation 1 from 2, then we have
0 = 3x – 5
3x = 5
x = 5/3
x = 1 2/3
Then the value of y will be
y = 5/3 + 3
y = 14 / 3
y = 4 2/3
Then the correct option is C.
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G
Express as a percent.
4/5%
Answer:
80%
Step-by-step explanation:
I'm assuming you meant express 4/5 as a percent and not 4/5%. So simply evaluate 4/5 to get 0.80. Now multiply this value by 100 to get the percentage which gives you 80%
Please help answer this question asap 3/11
The matrix elements are nothing more than the matrix entries. The correct option is B.
What is an element in a matrix?The matrix elements are nothing more than the matrix entries. They can be integers, variables, mathematical formulas, or any other type of character included within the matrix.
The value of a₁₄ is the value of the element of the given matrix, where 1 represents the row and 4 represents the column. Therefore, the value of a₁₄ is the element of the first row and the fourth column, which means the value of a₁₄ is 5.
Hence, the correct option is B.
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On the first journey, a cyclist travelled 1 1/2 km in x minutes.
On the second journey, the same cyclist travelled for y hours at the same average speed as on his first journey. Express, in terms of x and
total distance travelled in km for both journeys.
The equation D = 1.5x/y represents the total distance traveled in km in terms of x.
What is the 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:
On the first journey, a cyclist traveled 1 1/2 km in x minutes.
As we know,
Speed = distance/time
Distance = 1 1/2 = 3/2 km = 1.5 km
time = x
Speed = 1.5/x
On the second journey, the same cyclist traveled for y hours at the same average speed as on his first journey.
Distance = speed×time
Distannce(D) = (1.5/x)(y)
D = 1.5x/y
Thus, the equation D = 1.5x/y represents the total distance traveled in km in terms of x.
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Sam calculated (2.6 × 10 -2 )(1.5 × 10 -4 ) in his calculator. Which of the following results could be displayed on the calculator screen? Select all that apply.
3,900,000
0.0000039
3.9E6
3.9 × 10 -6
3.9E-6
The results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039
Evaluating an expressionFrom the question, we are to determine the results that could be displayed on the calculator screen
The given expression is
(2.6 × 10⁻²)(1.5 × 10⁻⁴)
= 2.6 × 1.5 × 10⁻²× 10⁻⁴
= 3.9 ×10⁻²⁺⁻⁴
= 3.9 ×10⁻²⁻⁴
= 3.9 ×10⁻⁶
= 3.9 E-6 OR 0.0000039
Hence, the results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039
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What do the points on the line in quadrant I represent in terms of the situation
Answer:
The points present in the first quadrant are of the form (a, b) where a, b>0.
Step-by-step explanation:
The points present in the first quadrant are of the form (a, b) where a, b>0.
In the first quadrant both the abscissa and ordinate are positive.
In the second quadrant the abscissa is negative and ordinate is positive.
In the third quadrant both the abscissa and ordinate are negative.
In the forth quadrant both the abscissa is positive and ordinate are negative.
The examples of points in the first quadrant are (1,0), (2,3), (11,4) and many other.
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Answer: The y-coordinates in the first quadrant are positive. because y represents the profit made, positive y values signify profit. The points in quadrant I represent the baseball team making a profit.
Step-by-step explanation: Source - I took the test.
Can you help find m<1
Answer:
69 degrees
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
<1 = 39+ 30
<1 = 69
Select the correct answer.
Consider the function represented in this table.
X
f(x)
-1
-21
0
-9
1
3
2
15
Which of these tables could represent the inverse of function f? Ahh
3.
The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.
Answer:
x = 5.00 cm
Step-by-step explanation:
• area of the rectangle = [tex]x[/tex] x [tex](x + 1)[/tex]
= [tex]x^2 + x[/tex]
• area of the circle = π r²
= [tex]\frac{22}{7}[/tex] x [tex](x + 2)^2[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4)[/tex]
∴ [tex]x^2 + x[/tex] + [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4) = 184[/tex]
⇒ [tex]x^2 + x[/tex] + [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]
⇒ [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]
• Using quadratic formula, where
a = [tex]\frac{29}{7}[/tex]
b = [tex]\frac{95}{7}[/tex]
c = [tex]\frac{-1200}{7}[/tex] ,
[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]
[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]
[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]
As length (x) cannot be a negative number,
x = 5.00 cm
Hey guys, need help here
Assuming [tex]a[/tex] is a non-negative real number...
Raise both sides to the power 2 :
[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^2 = 8^2 \implies a^{3/2} = 64[/tex]
which follows from the exponent product property, [tex](x^y)^z=x^{yz}[/tex]. In particular, 3/4 × 2 = 6/4 = 3/2.
Raise both sides to the power 1/3 :
[tex]\left(a^{3/2}\right)^{1/3} = 64^{1/3} \implies a^{1/2} = 4[/tex]
where we use the same property as before, and 4³ = 64. This time, 3/2 × 1/3 = 3/6 = 1/2.
Take the reciprocal of both sides. This negates the exponent, so we end up with
[tex]\dfrac1{a^{1/2}} = \dfrac14 \implies \boxed{a^{-1/2} = \dfrac14}[/tex]
Of course, you could also solve for [tex]a[/tex] immediately by raising both sides of the original equation to the power 4/3. We have 4/3 × 3/4 = 12/12 = 1, so
[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^{4/3} = 8^{4/3} \implies a = 8^{4/3}[/tex]
Now 2³ = 8, so [tex]8^{4/3} = \left(8^{1/3}\right)^4 = 2^4 = 16[/tex], and since 4² = 16, it follows that
[tex]a = 16 \implies a^{1/2} = \sqrt{16} = 4 \implies a^{-1/2} = \dfrac14[/tex]
Someone help me pleaseee
Answer:
A.) 588329.896
B.) 274300
C.) 1657.18474
D.) 1.002
(All answers unrounded.)
Explanation:
I converted each unit to the unit used in the other number (E.g., for question A I converted tons to kilograms, and then finished solving.)
What is the value of x?
Enter your answer in the box.
x =
Answer:
4
Step-by-step explanation:
In triangle JKL, the side opposite the 30 degree angle, JL, is half the length of the hypotenuse, KL. Thus, JL has a length of
[tex]4 \sqrt{2} [/tex]
In triangle JML, the hypotenuse is
[tex] \sqrt{2} [/tex]
times the length of the leg, meaning that x = 4
Select the correct answer.
Sammile pays $30 for a bag that she buys at a discount of 50% What is the price of the bag without the discount?
O A $30
O B. $45
O C. $60
O D. $80
If 30 is half price, then what is full price?
You can set up this problem like this:
30 = x/2
OR
30 = (1/2)x
where x is the full price.
To solve, simply multiply each half by 2:
2(30) = 2((1/2)x)
x = $60
Using your answer from the previous question, state the value of 't' if Josephine is going to run a dis-
tance of 15 miles at a rate of 5 miles per hour.
Previous answer t=d/r
Using the relation between velocity, distance and time, it is found that t = 3 hours.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
For this problem, the parameters are given as follows:
d = 15 miles, v = 5 mph
Hence the time in hours is found as follows:
[tex]v = \frac{d}{t}[/tex]
[tex]5 = \frac{15}{t}[/tex]
5t = 15
t = 15/5
t = 3 hours.
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Sin (5x-28) = cos (3x - 50)
By using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The question is incomplete.
The complete question is:
Solve for X given that sin(5X - 28)° = cos(3X - 50)°.
We have given:
sin(5X - 28)° = cos(3X - 50)°.
[tex]\rm \sin \left(5x-28\right)=\sin \left(\dfrac{\pi }{2}-\left(3x-50\right)\right)[/tex]
[tex]\rm \left5x-28\right= \left\dfrac{\pi }{2}-\left(3x-50\right)\right[/tex]
[tex]\rm x=\dfrac{4\pi n+156+\pi }{16}[/tex] (n = 0, 1, 2, ...)
[tex]\rm x=\dfrac{\pi +4\pi n-44}{4}[/tex]
Thus, by using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.
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PLEASE HELP ASAP
The value of "y" varies directly with "x" and
y=-8 when x = 20.
Find "y" if x = -4.
Enter the number that belongs in the green box.
Reduce to simplest form.
y = 2
Answer:
Just think of which number, when you multiply it with 20 will give you -8
and then you multiply that number with -4 to get y. Hope it helps!
bag contains one red pen, four black pens, and three blue pens. Two pens are randomly chosen from the bag and
are not replaced.
To the nearest hundredth, what is the probability that a black pen IS chosen first and then another black pen is
chosen?
ANSWER AT THE BOTTOM
Question:
There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.
Explanation:
Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.
Lets assume we picked a pen and got black.
Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.
For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.
The probability of rolling two 6's in a row is 1/36.
Lets apply the same principle to our situation right now.
So on the first draw, the probability is 1/2
And on the second draw, the probability is 3/7
1/2 MULTIPLIED BY 3/7 = 3/14
3/14 in decimal form is 0.21
ANSWER:
0.21, OR 21%
What should m<3 be for I1 II2
Answer:
63
Step-by-step explanation:
180 - 117 = 63 which is used to figure out angle 2.
Angle 2 and angle 3 are corresponding angles thus the measure of angle 3 is 63 degrees.
Answer:
Search up online
Step-by-step explanation:
i don't actually know but searching online is good
help grade 5 math please only answer if you know and if it’s right ill mark brainliest and please fast extra points who explain it
Answer:
[tex]\frac{42}{8}[/tex]
Step-by-step explanation:
7/8 <> 0.875
0.875 * 6 = 5.25
5.25 <> 42/8
(<> is used to show decimal to fraction and vice versa [the other way around])
Your are designing a rectangular birthday card for a friend. You want the card's length to be 1 inch more than twice the card's width. The area of the card is 88 square inches. What is the width of the card to the nearest tenth of an inch?
The width of the card to the nearest tenth of an inch is 6.15 inches
Area of rectangleWidth = xLength = 2x + 1Area = 88 square inchesArea of a rectangle = Length × Width
88 = (2x + 2) × x
88 = 2x² + 2x
2x² + 2x - 88 = 0
x = -b ± √b² - 4ac / 2a
= -2 ± √2² - 4(2)(-88) / 2(2)
= -2 ± √4 - (-704) / 4
= -2 ± √708 / 4
= -1/2 ± √177/2
x = 6.15 or -7.15 inches
The width of the rectangle can not be negative, so, 6.15 inches is the width.
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It takes 15 men, 48 days to weed a plot of land. How
의
plot of land in 16 days, if
mary men can weed the same
kry work at the sametime?
Answer:
it takes 48 days for 15 men to work
it takes 16 days for 15/48*16
the answer is 5 men
Answer:
45 men
Step-by-step explanation:
If you 1/3 the amount of time (from 48 to 16 ) to weed the plot, you will need to TRIPLE the number of men to 45 men
