1. Solve the following polynomial equations by factoring
b. x4+4x3-8x-32=0
Answers
\(x^4+4x^3-8x-32=0\)
Can be factoried into:
\((x^3-8)(x+4)=0\\\)
Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.
First we'll do:
\(x^3-8=0\)
We're looking for what number cubed is equal to 8, which is 2.
Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.
Second we'll do:
\(x+4=0\)
This one's pretty easy, x will be -4.
So your solutions are:
x = 2, -4
The solutions of the polynomial \(x^{4}\) + 4x³ - 8x - 32 = 0 are 2 and -4.
What is a polynomial?Polynomials are sums of terms of the form k⋅xⁿ.
where k is any number
n is a positive integer.
Example:
2x + 4x - 7 is a polynomial
We have,
\(x^{4}\) + 4x³ - 8x - 32 = 0 _______(1)
Divide into two parts.
\(x^{4}\) + 4x³
-8x - 32
Take out the common from each part.
x³ ( x + 4 )
- 8 ( x + 4 )
Now,
We have,
x³ ( x + 4 ) - 8 ( x + 4 ) = 0
We can write this as:
(x³ - 8) (x + 4) = 0
Now,
We need to find the x values.
x³ - 8 = 0
x³ = 8
x = ±2
Put x = 2 in (1)
\(x^{4}\) + 4x³ - 8x - 32 = 0
x = 2
16 + 32 - 16 - 32
0 = 0
x = 2 is satisfied
Put x = -2 in (1)
16 - 32 + 16 - 32 = 0
-64 ≠ 0
x = -2 is not satisfied
x + 4 = 0
x = -4 putting in (1)
256 - 256 + 32 - 32 = 0
0 = 0
x = -4 is satisfied
Thus the solutions of the polynomial \(x^{4}\) + 4x³ - 8x - 32 = 0 are 2 and -4.
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Related Questions
The graph of y = f(x) is shown below. According to the graph, what is f(4)?
Answers
Answer: 5
Step-by-step explanation:
When x=4, y=5.
This means f(4)=5.
Which shapes are similar but not congruent to shape 1
Answers
There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.
There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.
One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.
A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.
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WILL GIVE 5 STARS
Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer 45 minutes more than she plays golf.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day. (5 points)
Part B: How much time does Angela spend playing golf every day? (3 points)
Part C: Is it possible for Angela to have spent 80 minutes playing soccer every day? Explain your reasoning.
Answers
A: The linear equations are x + y = 125 and x = y + 45.
B: Everyday Angela spends 40 minutes in playing golf.
C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Part A:
Let x be the number of minutes Angela plays soccer every day
Let y be the number of minutes Angela plays golf every day
According to the problem statement the linear equations are -
x + y = 125 (total time playing both sports is 125 minutes)
x = y + 45 (Angela plays 45 more minutes of soccer than golf)
Part B:
Substitute x = y + 45 into the first equation -
(y + 45) + y = 125
Use the addition operation -
2y + 45 = 125
2y = 80
y = 40
Angela spends 40 minutes playing golf every day.
Part C:
If Angela spends 80 minutes playing soccer every day, then
x = 80
y + 45 = 80 (using the equation x = y + 45)
y = 35
But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.
This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.
Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.
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What is the asymptote of the exponential function graph below?
y=1
y=5
y=2
y=0
Answers
Answer: y=5 is the asymptote answer
1. Write an equation of the line in slope-intercept form that passes through (4.2) and (8.–2).
Answers
Answer:
its (8+4)/(-2-2) so the slope is -3x
Step-by-step explanation:
Which answer is the explict rule for the sequence? 12.5,11,9.5,8,6.5,5,...
Answers
Answer:
12.5, 11, 9.5, 8, 6.5, 5, ... 4. an = 14 − 1.5n
Step-by-step explanation:
Find the lengths of the sides of the triangle formed by the coordinates below. Then classify the triangle by sides.
A(1,1) B (4,1) C (4,5)
AB =
BC =
AC =
Number of congruent sides=
Then classify the triangle
Isosceles, scalene or equilateral
Answers
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad AB = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(4-1)^2+(1-1)^2}\implies AB=\sqrt{3^2-0^2}\implies AB=3 \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad BC=\sqrt{(4-4)^2+(5-1)^2} \\\\\\ BC=\sqrt{0^2+4^2}\implies BC=4 \\\\[-0.35em] ~\dotfill\)
\(C(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad A(\stackrel{x_2}{1}~,~\stackrel{y_2}{1})\qquad \qquad CA=\sqrt{(1-4)^2+(1-5)^2} \\\\\\ CA=\sqrt{(-3)^2+(-4)^2}\implies CA=\sqrt{3^2+4^2}\implies CA=5\)
well, how many congruent sides? none, all three sides differ, meaning is an scalene triangle.
A plane flying overhead at night is located by two
searchlights as shown at right. The two
searchlights are 1200 feet apart. Angle A = 72°
and angle B = 77º. How high is the plane?
Answers
Answer:
Step-by-step explanation:
B
2
3
Let the distance of two consecutive stones are x, x+1.
In ΔBCD, we have
tan60
o
=
x
h
⇒x=
3
h
.....(i)
In ΔABC, we have
tan30
o
=
x+1
h
⇒
3
1
=
x+1
h
⇒
3
h
+1=
3
h ......[from equation (i)]
⇒
3
2h
=1
⇒h=
2
3
km
solution
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°. What is the angle between the ground and steepest slope on the real rollercoaster?
Answers
The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?
To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.
The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.
The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.
That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)
The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.
That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,
the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°
The negative sign indicates that the angle is measured below the horizontal line.
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Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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Area of shaded region
Answers
Answer:
what are you asking
Step-by-step explanation:
PLZ HELP
Explain the difference between -2^4 and (-2)^4, and evaluate each power
and
Use your exponent rules to express as a single power, 94 ÷ 27^2
Answers
-2^4 = - (2x2x2x2) = -16
(-2^4) = -2 x -2 x -2 x -2 = +16
I NEED YOUR HELP!! I'LL. GIVE YOU BRAINLIEST
Answers
Answer: ∠16 and ∠11
Step-by-step explanation:
All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.
The correct corresponding angles are ∠16 and ∠11.
Chelsea played her tuba from 4:25 pm until 5:07
Answers
Answer:
42 minutes
Step-by-step explanation:
if you are asking how long it takes Chelsea to play her tuba then you do: 67 - 25 = 42
Answer:
Step-by-step explanation:
jhngjnh
If you dealt 4 cards from a shuffled deck of 52 cards without replacement, what is the probability that all 4 cards are face cards?.
Answers
The probability that all 4 cards are face cards is 0.00182842367.
The face cards are the King, Queen, and Jack (sometimes known as the Knaves). There are 12 face cards in the 52-card deck of playing cards.
The cards are drawn without replacement,
The probability of getting a face card in first draw is 12/52.
As it is without replacement, in the second draw the probability is 11/51.
In third draw, it is 10/50.
In the fourth draw the probability is 9/49.
We have to draw all the four cards, so we multiply the probabilities, to get the final probability.
=12/52x 11/51 x 10/50 x 9/49
=0.00182842367.
Therefore, the probability that all 4 cards are face cards is 0.00182842367.
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Find the weight in pounds of a 390 gram person.
Answers
Answer:
0.86 pound
Step-by-step explanation:
i just asked google:))
Help me pls!!!ASAP I don’t get it
Answers
Tony rents a bike that costs $4 per hour and $10 for the lock. He has $32 to spend. How long can he rent the bike? Write an equation that represents this situation. Be sure to explain how you got your equation and specify what the variables represent.
Answers
Answer:
5 hours; 4x+10=32
Step-by-step explanation:
4x = 4 multiplied by the amount of hours
10 = the cost for the lock
so y = 4x+10
In this case y= 32 so plug it in
4x+10=32
-10 -10
4x=22
/4 /4
x=5.5
So assuming you can only rent whole hours, it would be 5 hours
Hope this helps.
Answer:
he can rent the bike for 5 hours
Step-by-step explanation:
32-10=22
22*4=5
if mFI = 64 degrees and mRS = 180 degrees, find m
Answers
Yasmin purchased 6 heads of cabbage that each weighed 2 and StartFraction 3 over 8 EndFraction pounds. How much did the cabbage weigh all together?
9 and three-fourths pounds
12 and StartFraction 3 over 8 EndFraction pounds
13 and StartFraction 1 over 8 EndFraction pounds
14 and one-fourth pound
Answers
you would multiply 2 3/8 x 6= 14 2/8 = 14 1/4
Answer:
14 and one-fourth pounds
Step-by-step explanation:
edge 2021
Determine which set of side measurements could be used to form a triangle 13,19,7 25,12,13 18,2,24 3,1,5
Answers
The set of side measurements that could be used to form a triangle are;
18, 2, 243, 1, 5What is a triangle?A triangle is a three sided polygon that also has three interior angles.
The set of sides measurements that could be used to form a triangle can be obtained from the Sides of Triangle Rule as follows;
The Sides of Triangle Rule states that in a triangle, the sum of the lengths of two sides is always larger than the length of the third side, therefore, in a triangle with sides, a, b, and c, where c is the longest side, we get;
a + b > c
The length of the sides that form a triangle, based on the Sides of Triangle Rule are found as follows;
13 + 7 = 20 > 19;The first set of sides can not be used to form a triangle
12 + 13 = 25; The second set can not be used to form a triangle
18 + 2 = 20 < 24; The third set, 18, 2, 24 can be used to form a triangle
3 + 1 = 4 < 5; The fourth set can be used to form a triangle
The set of sides that can be used to form a triangle are;
18, 2, 24, and 3, 1, 5
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What is the length of side a? Round to the nearest tenth of an inch. Enter your answer in the box.
Answers
9514 1404 393
Answer:
14.4
Step-by-step explanation:
The Pythagorean theorem tells you ...
7² +a² = 16²
a² = 256 -49
a = √207
a ≈ 14.4
Place value of 4 in 265 473
Answers
Answer:
The place value of 4 in 265 473 is 40,000
Answer:
Step-by-step explanation:
Order:
3 is in the ones place and has a value of 3
7 is in the tens place and has a value of 70
4 is in the hundreds place and has a value of 400
5 is in the thousands place and has a value of 5000
6 is in the ten thousands place and has a value of 60,000
2 is in the hundred thousands place and has a value of 200,000
Find x (circle)
(Btw I don’t know if 5.6 is correct so just ignore that)
Answers
Answer:
A. 11.2
Step-by-step explanation:
But this has nothing to do with 5.6 × 2. Erase that! Lol.
You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.
The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.
The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.
The hypotenuse is 14.
Let's do some Pythagorean Theorem.
Leg^2+ leg^2=hypotenuse^2
you know,
a^2 + b^2 = c^2
fill in what we know.
8.4^2 + b^2 = 14^2
simplify.
70.56 + b^2 = 196
subtract 70.56
b^2 = 125.44
squareroot both sides
b = 11.2
What is the value of x to the nearest tenth?
Answers
Answer:
x ≈ 2.5
Step-by-step explanation:
Use tan∅ to solve this problem:
tan23° = x/6
x(tan23°) = x
x = 2.54685
FIND THE AREA PLEASE HELP ILL GIVE BRAINLIESTTTT
Answers
Answer:
28.8 yd^2
Step-by-step explanation:
The area of a triangle is calculated using the following formula:
1/2*b*h (b: base, h: height)
The height in this triangle is 6.4 yd and the base is 9 yd
1/2*9*(6.4) = 28.8
What is the value of x?
OA) 65°
B) 50°
OC) 80°
OD) 90°
Answers
Answer:
Please mark be Brainliest and I hoped this helped!
x = 80°
Step-by-step explanation:
These are both isosceles triangles, so the top 2 angles are both 65°. The last angle of that triangle is 180° - (65° + 65°) which is 50°. Then, the opposite of that angle is in the next triangle. It is also 50°. So the 2 base angles are both 50°, so x is 180° - (50° + 50°) which is 80°.
An ion has a charge of +7. How far is it from being neutral?
A. -0.07
B. -7
C. 7
D. 70
E. 0.7
Answers
Ashley is training to run a marathon. On Monday, she runs 21 miles in 3 hours. On Wednesday, she runs 10 1/2 miles in 1 1/2 hours. What is the constant of proportionality in miles per hour?
Answers
Answer:
10.5 mph
Step-by-step explanation:
To find the constant of proportionality in miles per hour, we need to divide the distance (in miles) by the time (in hours) for each of the two runs, and then take the average of the two rates.
For Monday's run:
Rate = Distance / Time = 21 miles / 3 hours = 7 miles per hourFor Wednesday's run:Rate = Distance / Time = 10 1/2 miles / 1 1/2 hours = (21/2) miles / (3/2) hours = 14 miles per hour
To find the average rate, we add the two rates and divide by 2:Average rate = (7 miles per hour + 14 miles per hour) / 2 = 10.5 miles per hour
Therefore, the constant of proportionality in miles per hour is 10.5. This means that Ashley runs at an average rate of 10.5 miles per hour during her training.
There are 126 animals on the farm. If each animal eats 7 packages of food each week, how
many
packages of food should the farmer buy each week?*
Answers
Answer:
882 packages
Step-by-step explanation:
126×7= 882