Answer:
[tex]b = 2[/tex].
Step-by-step explanation:
By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].
Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:
[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].
Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:
[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].
Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:
[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].
[tex]b = 2[/tex].
Reduce the fraction, then change to a mixed number. 20/3
[tex] \frac{20}{3} [/tex]
To find:[tex] \frac {20}{3} [/tex] as a mixed number.
Solution:First, divide the numerator by the denominator.
[tex]20 \div 3 [/tex]
[tex] = 6 \: R2[/tex]
Then, write the whole number value and use the remainder as the numerator over the denominator. As we all know the denominator won't change.
[tex]\large\boxed{\sf{= 6 \frac{2}{3}}}[/tex]
Hellppppppppppllpppp
Answer:
180 in^2
Step-by-step explanation:
S=(1/2)lP + B
B = 10x10 = 100
P = 10(4) = 40
l is 4, but you could also use the fact that each triangular side is A=(1/2)bh.
(1/2)4 x 10 = 20
20(4) = 80
add 100 + 80 = 180
Susan got to the school bus stop at 6:08, she waited 1 minute for the bus. What time was it when Susan’s bus came?
Answer:
6:09
Step-by-step explanation:
6:09 is one minute after 6:08
Which of the following expanded forms represents the number words one thousand, six hundred eighty-nine?
O 1,000 + 60 + 80 + 9
O None of thse choices are correct.
O 600 + 80 + 9
O 1,000 + 600 + 80 + 9
O 1,000 + 60 + 8 + 9
This window is designed in the shape of a right trapezoid.
Answer: 128°
Step-by-step explanation:
There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.
360° = 90° + 90° + 52° + x°
360° = 90° + 90° + 52° + x°
360° = 232° + x°
128° = x
x = 128°
The obtuse angle has a measure of 128°.
The pool company has learned that, by pricing a newly released Fun Noodle at $5, sales with reach 8000 Fun noodles per day during the summer Raising the price to $6 will cause the sales to fall to 5000 fun noodles per day
Please help! Evaluate y = (x + 3)(x – 2) at x = r1 and then at x = r2. Show your work below.
The values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively
How to evaluate the function?The function is given as:
y = (x +3)(x - 2)
When x = 1, we have:
y = (1 +3)(1 - 2)
y = -4
When x = 2, we have:
y = (2 +3)(2 - 2)
y = 0
Hence, the values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively
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A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%, how many dollars is the sale price of the car
If there is 15% off and the sales tax rate is 8.25%. Then the price of the car will be $ 8,189.11.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%.
The cost after 15% off will be
→ 0.85 × $8,900
→ $ 7,565
Then the final cost after the sale tax of 8.25% will be
Cost = $ 7,565 × 1.0825
Cost = $ 8,189.11
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josiah is running a marathon which is 26 1/5 miles Long. At four 1/4 miles from the start, he meets his wife, who is cheering him on. 7 1/2 miles further down the marathon course, he sees some Friends from his running club volunteering at a water stop. Once he passes his friends, how many more miles does Josiah have left to run?
Once he passes his friends, The miles Josiah has left to run would be 10.95 miles.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Josiah is running a marathon which is 26 1/5 miles long.
At four 1/4 miles from the start, he meets his wife, who is cheering him on.
7 1/2 miles further down the marathon course.
26 1/5 = 131/ 5
7 1/2 = 15/2
The marathon run by Josiah
= 1/4 + 15/2
= 15.25
The miles Josiah has left to run
= 131/ 5 - 15.25
= 10.95
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Find the surface area of a cylinder with a height of 5 ft and a base radius of 4 ft.
Use the value 3.14 for x, and do not do any rounding.
Be sure to include the correct unit.
Answer:
A =281 ft^2
Step-by-step explanation:
A=2πrh+2πr^2
A = 2 (3.14) (4)(5) + 2 (3.14) (5)^2
A =281 ft^2
A triangle has a base length of 6ac² and a height 3 centimeters more than the base length. Find the
area of the triangle if a = 2 and c=3.
Hey there!
EQUATION:
6ac^2
ASSUMING:
= 6(2)(3)^2
SOLVING:
= 6(2)(3^2)
= 12(3^2)
= 12(3 * 3)
= 12(9)
= 108
Therefore, the answer should be: 108
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
4. For v = -2i – 7j, find the unit vector in the direction of y, and write your answer as a linear combination of the standard unit vectors i and j
5. Find u•v if u = i + 2j and v = -i + 5j.
4. If v = -2i - 7j, then its magnitude is
||v|| = √((-2)² + (-7)²) = √53
and the unit vector in the direction of v is
[tex]\dfrac{v}{\|v\|} = \boxed{-\dfrac2{\sqrt{53}} \, \vec\imath - \dfrac7{\sqrt{53}} \, \vec\jmath}[/tex]
5. Given u = i + 2j and v = -i + 5j, we have
u • v = (i + 2j) • (-i + 5j) = -(i • i) - 2 (j • i) + 5 (i • j) + 10 (j • j)
Since i and j are orthogonal unit vectors, we have i • i = j • j = 1 and i • j = 0, so the product reduces to
u • v = -1 - 0 + 0 + 10 = 9
(05.07) A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
The surface area of the square based pyramid is 61.25 centimetre square
How to find the surface area of a square base pyramid?surface area of the pyramid = A + 1 /2 ps
where
A = area of the base
p = perimeter of the base
s = slant height
Therefore,
A = 3.5² = 12.25 cm²
p = 4(3.5) = 14 cm
s = 7 cm
Therefore,
surface area of the pyramid = 12.25 + 1 /2 × 14 × 7
surface area of the pyramid = 61.25 cm²
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Jan's electric bill is averaging $8 per day mostly due to the air conditioner. By setting the AC to a higher temperature, closing curtains to block sunlight, and using direct-blowing fans for comfort, Jan reduces the bill to $5 per day. How much did Jan reduce the electric bill for a 30-day month?
Answer:
$5×30days= $150 for the whole month
Answer: $90 saved
Step-by-step explanation:
8 - 5 = $3 dollars saved each day
Multiply daily amount saved by number of days
$3 × 30 = $90 saved
This is had can you help me
Answer:
#9 is 6 #10 is 1 #11 is 7 #12 is 6
Step-by-step explanation:
A weighted (unfair) die that was purchased at a magic shop was rolled 30 times. The die landed on five dots 25 times. Based on the results, what is the margin of error for the true proportion of times this die would land on five dots? Base your margin of error on a 95% confidence level.
Using the z-distribution, it is found that the margin of error for the true proportion of times this die would land on five dots is of 0.1338.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size are given as follows:
[tex]\pi = \frac{25}{30} = 0.8333, n = 30[/tex].
Hence the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.8333(0.1667)}{30}}[/tex]
M = 0.1338.
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the value of a varies directly as the square of the value of b, and b=3 when a=10. Find the value of a when b=9.
Answer:
answer = 90
Step-by-step explanation:
General equation: a = k*b^2
Specifically: 10 = k*(3)^2 = 9 k
Solving for k: k = 10/9
Then a = (10/9)b^2. If b = 9, then a = (10/9)(9)^2 = 90 (answer)
Use proportional thinking to answer the question. Explain how you got an answer without using pencil and paper or a calculator.
If 10% of a number is 4.3, what is
20% of the number?
Answer:
8.6
Step-by-step explanation:
If we know 10% of a number is 4.3, we can easily find 20% of the number as well.
We know 20% is 2 times 10%.
Therefore,
2 x 4.38.6can you help this is hard
Answer:
y=1/2x+1= A
y=-2x-4= C
x-2= E
y=-3= F
y=1/2x+3.5=B
I hope this helps
Step-by-step explanation:
Show that if AB=DC in the figure below, then AB is parallel to CD.
AB is parallel to CD because the figure is a parallelogram and opposite sides of a parallelogram are parallel.
What are the properties of a parallelogram?Note, the figure is a parallelogram
Some properties of a parallelogram are:
The opposite sides of a parallelogram are parallel and equal.The opposite angles are equal.The consecutive angles are supplementary, that is, the sum up to 180°The two diagonals divide each other.if sides AB = DC, then AB is parallel to CD because they are opposite to each other and opposite sides of a parallelogram are parallel.
Hence, AB is parallel to CD because the figure is a parallelogram and opposite sides of a parallelogram are parallel.
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can anyone answer this? i’ve had multiples tutors and none have been able to help.
Answer:
Area = 3430
Step-by-step explanation:
Graphing y = 28x - x^2 with it's limit interval (0<x<28). They ask for four sub-interval of LRAM.
Divide the base of 28 into 4 equal rectangles.
Area = (Base * Height) + (Base * Height) + (Base * Height) + (Base * Height)
Area = (0 * 7) + (147 * 7) + (196 * 7) + (147 * 7)
Area = 3430
what is 4,649 divided by 39
Answer:
[tex]4649 \div 39 = 119.205128295[/tex]
Step-by-step explanation:
I hope it's help u
Answer:
119 R 8
Step-by-step explanation:
convert 4649 to tens place, write 1
46 - 39 = 7
drop the 4 in the tens place, write 1
74 - 39 = 35
drop the 9 in the ones place, write 9
359 - 351 = 8
• For each time we got 39 or another number, we wrote the multiple of that number we used to get the result.
• We got the remainder by the general subtraction.
Tory’s expenses of $300 in May were at least $40 less than twice her expenses in April. What is the least possible amount of her expenses in April?
Evaluate: [tex]\sqrt{100-36} + 32 - 1[/tex]
Precalculus based question.
Answer:
39
Step-by-step explanation:
[tex]\sqrt{100-36}+32-1\\\sqrt{64}+31\\8+31\\39[/tex]
Hey there!
√(100 – 36) + 32 – 1
= √(64) + 32 - 1
= 8 + 32 – 1
= 40 – 1
= 39
Therefore, the answer should be: 39
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
find the value of 7x+2y when x=2 and y=-9
Answer:
32
Step-by-step explanation:
7×18+2×18=32
x=14
y=18
Have a great day!
There is a population of 15,500 bacteria in a colony. If the number of bacteria doubles every 234 hours, what will
che population be 936 hours from now?
bacteria
Answer:
2,48,000
Step-by-step explanation:
Initial population of bacteria = 15,500Bacteria doubles after every 234 hoursSo, after 0 (zero) hours, no of bacteria = 15,500After 234 hours, no. of bacteria = 2(15,500) = 31,000After 468 hours, no. of bacteria = 2(31,000) = 62,000 (2*234 = 468)After 702 hours, no. of bacteria = 2(62,000) = 124,000 (3*234 = 702)After 936 hours, no. of bacteria = 2(124000) = 2,48,000 (4*234 = 936)Kate has a box of red nibbon and bhie ribbons The ratio of red ribbons to total ribbons is 5 14 Choose all the statements that are true about Katie's box of ribbons
(A The ratio of total ribbons to blue ribbons is
14:9
(B. The ratio of red ribbons to blue ribbons is 9:5
(C. The ratio of total ribbons to red ribbons is 14:5
(D. There must be 9 more blue ribbons than red ribbons
(E. The ratio of blue ribbons to red ribbons is 9,5
What is the value of x?
Answer:
a) 20
Step-by-step explanation:
90 - 46 = 44
44 - 4 = 40
40/2 = 20
The scale factor of a model car to the actual car is 300. If the model car is 2in tall, how tall is the actual car?
Answer:
600 inches or 50 feet
Step-by-step explanation:
Scale factor = model car : actual car = 1 : 300
We have a 2 inch model car.
2 in. : actual = 1 : 300actual = 2 × 300actual = 600 inches or 600/12 = 50 feetA circular tabletop has a circumference of 94.2 inches. What is its approximate area?
Answer:
1st choice : 706.5 square inches
Step-by-step explanation:
circumference is pi times diameter
divide 94.2 by pi to get diameter = 29.9847912785
diameter 29.9847912785 divided by 2 is
14.9923956393 which is the radius
area is pi times radius times radius again
pi times 14.9923956393 times 14.9923956393 =
706.141834613