Answer:
a(87) = -590
Step-by-step explanation:
Notice how each term of this arithmetic sequence is equal to the sum of the previous term and the common difference, -12.
The general formula a(n) = a(1) + (n - 1)d becomes:
a(n) = 12 - 7(n - 1)
and the 87th term a(87) = 12 - 7(87 - 1), or
a(87) = 12 - 7(86)
a(87) = -590
1. Find the numbers a, b, c such that
2x4 + 2x3 +5x2 + 3x + 3 = (x2 + x +1)(ax2+bx+c)
for all values of x.
Answer:
a = 2
b = 0
c = 3
Step-by-step explanation:
if I understand correctly the problem should look like
2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)
let's calculate the right side
ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c
as there is only one term of x⁴, we know a = 2
as there is only one term without any x, we know c = 3
now we get
2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3
remember, that is equal to
2x⁴ + 2x³ + 5x² + 3x + 3
after subtracting 2x⁴ and 3 from both sides we get
2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x
we subtract 2x³ and 3x from both sides and get
5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx
we subtract 5x² from both sides and get
0 = bx³ + bx² + bx
=> b must be 0 to make this true for all values of x
please help! 10 points and brainlyist!!
Answer:
1.80 in^3
1.0 fluid ounces^3
Step-by-step explanation:
volume of a cone = 1/3 πr²h
π = 3.14
r = 2.2 / 2 = 1.1
h = the value of h can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
1.8² = 1.1² + b²
3.24 = 1.21 + b²
3.24 - 1.21 = b²
2.03
b = √2.03 = 1.42
Volume = 1/3 x 3.14 x 1.21 x 1.42 = 1.80 in^3
1.80 x 0.554 = 1.0 fluid ounces^3
Which represents the table ?
Answer:
b
Step-by-step explanation:
dfghdfhjdfjdfj
please help!!
find x
Answer:
since the square indicates the angle is a right angle ( 90 ° )
then x = 90 - 32
x = 58 °
which inequalities pairs with y<-2x-1 to complete the system of linear inequalities represented by the graph?
There is a geometrical relation that arc of circle is equal to the central angle.
And there is another relation that arc of a circle is equal to (radius *arc)
Aren't these two relation conflicting?
What is the vaule of tan-240 degrees?
What's the surface area of the pyramid?
The Answer is C 226.8 ft
I remember doing this not to long ago
Jasmine drew triangles on a globe and on a flat map of the world, as shown below.Which is a true statement comparing Jasmine’s two drawings?
A. The angle sum of the triangle on the globe is equal to the angle sum of the triangle on the map.
B. The angle sum of the triangle on the globe is greater than the angle sum of the triangle on the map.
C. The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe.
D. There is only one line connecting New York to Paris on the map but more than one line connecting New York to Paris on the globe
Answer:
B
Step-by-step explanation:
OEMJIGOVNarioendsdmarfwsipf JUST BELIEVE, also looking is good
The true statements on comparing Jasmine’s two drawings are B and C.
What is Angle Sum Property of a Triangle ?The sum of a finite traingle's interior angle is equal to 180° and this is called the Angle Sum Property of a Triangle.
It is given in the question
Jasmine drew triangles on a globe and on a flat map of the world
On comparing both the triangle the conclusions are
The triangle drawn on the globe is a spherical triangle and the angle sum of the interior angle will be greater that the two right angles or 180°.
Among the option given this is also true that
The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe
Therefore option B and C are both true statement comparing Jasmine’s two drawings .
To know more about Angle Sum Property
https://brainly.com/question/8492819
#SPJ2
Which side lengths form a right triangle?
Answer:
answer is option B
9² +40² =41²
81+1600=1681
Answer:
B) 9 , 40, 41
............
PLEASE I NEED THE ANSWER DON'T IGNORE MY QUESTION!!!
Answer:
x=7.8
Step-by-step explanation:
take 49 degree as reference angle
using cos rule
cos 49=adjacent/hypotenuse
0.65=x/12
0.65*12=x
7.8=x
Answer:
x=7.8
Step-by-step explanation:
Step-by-step explanation:
take 49 degree as reference angle
using cos rule
cos 49=adjacent/hypotenuse
0.65=x/12
0.65*12=x
7.8=x
If the equation 2x2+bx+5=0 has no real solutions, which of the following must be true?
Answer:
There are no choices but in order to qudratic equation not to have real roots the discriminant must be negative.
d = b² - 2*2*5 = b² - 20If d < 0, we get:
b² - 20 < 0b² < 20b < |√20|- √20 < b < √20or
-2√5 < b < 2√5or
b = (-2√5, 2√5)the difference of two numbers is 13/24. if 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other, what are the 2 numbers?
Answer:
The two numbers are 11/8 and 5/6
Step-by-step explanation:
Let the unknown numbers be x and y
Given that the difference of two numbers is 13/24
x - y = 13/24
and that 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other
11/12 * 1/x = 5/9 * 1/y
11/12x = 5/9y
cross multiply
12x * 5 = 11* 9y
60x = 99y
x = 99y/60
= 33y/20
substitute into x - y = 13/24
33y/20 - y = 13/24
13y/20 = 13/24
24y = 20
y = 20/24
= 5/6
x = 33y/20
= 33 *5/20*6
= 11/8
Kevin is doing a puzzle. He has completed 89/100 of the puzzle. Which decimal represents how much of the puzzle Kevin has left to do?
Answer:
100-89/100=11/100
=0.11
Logx-1(343)=3 solve for base x
Answer:
should be 8 !
Step-by-step explanation:
it just is
–6(2 + a) = –48 please answer
Answer:
a = 6
Step-by-step explanation:
–6(2 + a) = –48
Divide each side by -6
–6(2 + a) / -6 = –48/-6
2+a = 8
Subtract 2 from each side
2+a-2 = 8-2
a = 6
Box A has 14 black pens and 6 blue pens box B has 9 black pens and 3 blue pens a pen is randomly chosen from each box list these events from least likely to most likely
Answer:
The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
Black - Black
Black - Blue
Blue - Black
Blue - Blue
Probability of each outcome:
Black-Black:
14 out of 20, and then 9 out of 12. So
[tex]P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}[/tex]
Black-Blue:
14 out of 20, then 3 out of 12. So
[tex]P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}[/tex]
Less likely than black-black.
Blue - Black:
6 out of 20, then 9 out of 12. SO
[tex]P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}[/tex]
More likely than black-blue, less likely than black-black.
Blue - Blue
6 out of 20, then 3 out of 12
[tex]P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}[/tex]
Least likely of the outcomes.
List these events from least likely to most likely:
The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black
Belinda gets 1 3/4 h for lunch. She spends 1/3 of her lunch walking for exercise. How much time does Belinda spend walking ?
This unit is operations and fractions how would I solve this?
Answer:
7/12 h
Step-by-step explanation:
1/3 of 1 3/4 = 1/3 of 7/4 = 1/3 x 7/4 = 7/12 h
A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Nicole grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 23 ft.) Round to the nearest tenth of a foot.
The ladder will reach a height of 20.6 feet
The given parameters are:
Length = 45-footHeight = 27 feetStart by calculating how far (d) the ladder is, from the bottom of the house using the following Pythagoras theorem
[tex]45^2 = 27^2 +d^2[/tex]
Collect like terms
[tex]d^2= 45^2 -27^2[/tex]
[tex]d^2= 1296[/tex]
Take square roots of both sides
[tex]d= 36[/tex]
When the ladder is moved 4 feet farther, the new distance becomes
[tex]d= 36+4[/tex]
[tex]d= 40[/tex]
The new height (h) of the ladder is then calculated using the following Pythagoras theorem
[tex]45^2=40^2 + h^2[/tex]
Collect like terms
[tex]h^2 = 45^2-40^2[/tex]
[tex]h^2 = 425[/tex]
Take the square roots of both sides
[tex]h = 20.6[/tex]
Hence, the ladder will reach a height of 20.6 feet
Read more about Pythagoras theorem at:
https://brainly.com/question/654982
help mi plzz.........
A penny is dropped from a point on a bridge 94 feet above the surface of the river. If the penny travels 250 feet straight down before it lands at the bottom of the river, find the depth of the river where the penny landed.
please provide with the strategies please!!
Answer:
156 ft
Step-by-step explanation:
the depth of the river =
250-94 = 156 ft
Please Help. It would be very helpful to me
Answer:
A) 2 inches
Step-by-step explanation:
Raju's father is 26 years younger than raju's grandfather and 29 years older than raju. The sum of the ages of all the three is 135 years. Also raju's grandmother is 4 times raju's age and his sister is 7 times younger than him
Answer:
Raju = 17 years
Raju's father age = 46 years
Raju's grandfather age = 72 years
Raju's grandmother = 68 years
His sister = 10 years old
Step-by-step explanation:
Raju’s father is 26 years younger than Raju’s grandfather and 29 years older than Raju. The sum of the ages of all the three is 135 years. Also, Raju's Grandmother is four times of Raju’s age and his sister is 7 years younger than him.
Let
Raju's age = x
Raju's father age = x + 29
Raju's grandfather age = (x + 29) + 26
Total ages = 135
(x) + (x + 29) + (x + 29) + 26 = 135
x + x + 29 + x + 29 + 26 = 135
3x + 84 = 135
3x = 135 - 84
3x = 51
x = 51 /3
x = 17
Raju's age = x = 17 years
Raju's grandmother = 4 times raju's age
= 4 × 17 years
= 68 years
his sister = 7 years younger than him.
= 17 - 7
= 10 years old
Raju's father age = x + 29
= 17 + 29
= 46 years
Raju's grandfather age = (x + 29) + 26
= 46 + 26
= 72 years
Helppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
4.4
Step-by-step explanation:
that is the procedure above
work out the m and c for the line: y=x-7
Answer:
Step-by-step explanation:
Compare the given y = x - 7 to the general slope-intercept formula
y = mx + b
Here the slope is 1 and the y-intercept, b, is -7.
Answer:
Step-by-step explanation:
Slope - y intercept form : y = mx +c
y = x - 7
m = 1
c = -7
y/7 + 2.1 = 9.1
solve for y.
Answer:
-79
Step-by-step explanation:
-9.1-2.1=-11.2
--79÷7=-11.2
Answer:
y = -78.4
Step-by-step explanation:
y/7+2.1-2.1=-9.1-2.1
y/7=-11.2
y/7*7=-11.2*7
y= -78.4
How many feet is it from goal line to goal line on a regulation football field
that is 100 yards long? It is measured in the
A. tens
B. thousands
C. millions
D. hundreds
Answer:
D. hundreds
Step-by-step explanation:
if a football field is 100 yards long then it is 300 feet long and that is in the hundreds
Here are 2 right triangles.
9
S
у
a. Explain how you know the right triangles are similar.
Type your response in the space below.
В І о
B
Answer:
Step-by-step explanation:
They are similar because they have two respective congruent angles
Write an expression for the phrase.
The product of n and negative 3
A line passes through the points (-2, 4) and (6, 16). Which of the following would not be
a correct equation of the line?
