Answer:
139
Step-by-step explanation:
He originally had 147 books and threw 8 into a pond.
147-8=139
Find the specified value for the arithmetic sequences with the given characteristics. a17 = 47 d = -3 a35= ?
ANSWER
The 35th term is -8
EXPLANATION
The nth term of an arithmetic sequence is given by
[tex]a_n = a_1 + d( n - 1)[/tex]
We have the 17th term to be;
[tex]a_{17}=47[/tex]
and the common difference is d=-3
We substitute to get:
[tex]47= a_1 + - 3(1 7- 1)[/tex]
[tex]47= a_1 + 16( - 3)[/tex]
[tex]47= a_1 - 48[/tex]
[tex]a_1 = 48 + 47 = 95[/tex]
We can now find the 35th term:
[tex]a_{35}=a_{1} + 34d[/tex]
[tex]a_{35}=95 + 34( - 3) = - 8[/tex]
A traffic camera sits on top of a tower that has a height of 50ft., the angles of depression of two cars on a straight road at the same level as that of the base of the tower and on the same side of it are 25° and 40°. Calculate the distance between two cars
Answer:
[tex]\boxed{\text{48 ft}}[/tex]
Step-by-step explanation:
The angle of depression from the camera at D and the angle of elevation from the target cars are congruent.
1. Distance of car A from tower
Consider ∆ACD
tan25 = 50/AC
AC = 50/tan25 = 50/0.4663 = 107.2 ft
2. Distance of car B from tower
Consider ∆BCD
tan40 = 50/BC
AC = 50/tan40 = 50/0.8391 = 59.6 ft
3. Distance from cars A and B
AB = AC – BC = 107.2 – 59.6 = 48 ft
The distance between the two cars is [tex]\boxed{\textbf{48 ft}}[/tex].
Find the slope of a line parallel to 2x-y=18
Answer:
The slope of line parallel to 2x-y = 18 will be 2.
Step-by-step explanation:
Given
The equation of a line : 2x – y = 18
The standard form of an equation of a line in slope-intercept form is:
y=mx+c
So, we will have to convert the given equation in the standard form.
2x-y=18
-y=-2x+18
-y= -(2x-18)
y=2x-18
The coefficient of x in this form is the slope of the line.
So,
m_1=2
We know that slopes of two parallel lines are equal so if the given line has slope 2, all the lines parallel to this line have slope 2..
For this case, we have by definition, if two lines are parallel then their slopes are equal:
[tex]m_ {1} = m_ {2}[/tex]
We have the following equation:[tex]2x-y = 18[/tex]
We rewrite the equation of the form:
[tex]y = mx + b\\2x-18 = y\\y = 2x-18[/tex]
Thus, a parallel line will have a slope [tex]m_ {2} = 2[/tex]
Answer:
[tex]m_ {2} = 2[/tex]
Transform each polar equation to an equation in rectangular coordinates and identify its shape.
(a) r=6
(b) r= 2 cos theta
please show ur work
Answer:
(a) [tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]
(b) [tex](x-1) ^ 2 + y ^ 2 = 1[/tex]
Step-by-step explanation:
Remember that to convert from polar to rectangular coordinates you must use the relationship:
[tex]x = rcos(\theta)[/tex]
[tex]y = rsin(\theta)[/tex]
[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]
In this case we have the following equations in polar coordinates.
(a) [tex]r = 6[/tex].
Note that in this equation the radius is constant, it does not depend on [tex]\theta[/tex].
As [tex]r ^ 2 = x ^ 2 + y ^ 2[/tex]
Then we replace the value of the radius in the equation and we have to::
[tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]
Then [tex]r = 6[/tex] in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].
(b) [tex]r = 2cos(\theta)[/tex]
The radius is not constant, the radius depends on [tex]\theta[/tex].
To convert this equation to rectangular coordinates we write
[tex]r = 2cos(\theta)[/tex] Multiply both sides of the equality by r.
[tex]r ^ 2 = 2 *rcos(\theta)[/tex] remember that [tex]x = rcos(\theta)[/tex], then:
[tex]r ^ 2 = 2x[/tex] remember that [tex]x ^ 2 + y ^ 2 = r ^ 2[/tex], then:
[tex]x ^ 2 + y ^ 2 = 2x[/tex] Simplify the expression.
[tex]x ^ 2 -2x + y ^ 2 = 0[/tex] Complete the square.
[tex]x ^ 2 -2x + 1 + y ^ 2 = 1[/tex]
[tex](x-1) ^ 2 + y ^ 2 = 1[/tex] It is a circle centered on the point (1, 0) and with radio [tex]r=1[/tex]
how far will john travel if he drives for 2 and a half hours at 55mph?
Answer:
137.5 miles
Step-by-step explanation:
1. Do 55/2 to account for the half hour.(should equal 27.5)
2. Do 55 x 2 to account for the 2 hour drive.(should equal 110)
3. Add everything up. 110 + 27.5 = 137.5 miles
ANSWER
137.5kmi
EXPLANATION
The relation between speed , time and distance is given by the relation:
[tex]speed = \frac{distance}{time} [/tex]
Therefore
Distance= speed × time
John was traveling at a speed of 55mph
for 2 ½ hours.
The distance covered will be:
=55×2.5mi
=137.5mi
Factorise x^2+14x+24 PLS HELP
Answer:
(x + 12)(x + 2)
Step-by-step explanation:
In order to factorize, we first have to break the term in the middle into two terms which add up to 14 and and multiply to 24.
For this, let's take a look at the factor pairs of 24. We have (1, 24), (2,12), (3, 8), (4, 6).
note that the 2nd pair works. 2 + 12 = 14, 2*12 = 24.
And now we rewrite the expression.
x^2 + 14x + 24
= x^2 + 12x + 2x + 24
Take out common factors as below
= x(x + 12) + 2(x + 12)
Note that (x+12) is a common factor in the 2 added expressions. So we take it out.
= (x+12)(x+2)
Done!!! Hope it helps, and if it does, please mark me brainliest...
What is the simplified form of (4j^2+6)+(2j^2-3) ?
1. 6j^2-3
2. 6j^2+3
3. 6j^2+9
4. 4j^4+3
Answer:
2. 6j^2 + 3
Step-by-step explanation:
help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
It looks like w = 0 which is the value of the x intercept.
If that is so, there was 2500 dollars in the safe to being with.
answer b//////////////////
Let f(x)=x^2+1. Let g(x)=(x+2)^2+1. Which statement described the graph of g(x) with respect to the graph of f(x)?
compressed vertical by a factor of 2
translated left 2 units
translated right 2 units
compressed horizontal by a factor
Answer:
translated left by 2 units
Step-by-step explanation:
Given y = f(x) then
y = f(x ± a) represents a horizontal translation of a units
• If + a then a shift of a units to the left
• If - a then a shift of a units to the right
Hence
g(x) is the graph of f(x) translated 2 units to the left
The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. It represents a translation of the graph of f(x) to the left by 2 units.
Explanation:The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. Particularly, it's a horizontal shift, not a compression or stretching of the graph. By comparing coefficients, we infer that the +2 inside the parentheses on g(x) represents a shift of the graph of f(x) to the left by 2 units. This is because the rules of transformations dictate that h(x) = (x - h)^2, where h represents a shift to the right, and h(x) = (x + h)^2 represents a shift to the left. Therefore, the correct statement is that the graph of g(x) is translated left 2 units compared to the graph of f(x).
Learn more about Function Transformation here:https://brainly.com/question/37849754
#SPJ2
need helpppppppppp pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
320 cubic cm
Step-by-step explanation:
To answer a prism volume question, also see it as a shape (in this case a triangle) that is very thick.
First step is to calculate the area of the shape. We all know the formula to calculate the area of a triangle: (b x h)/2. And we those two measures. The height of the triangle is b (8 cm), the base of the triangle is a (10 cm).
A = (b * h)/2 = (10 * 8) / 2 = 80 / 2 = 40 sq cm
Then we multiply the base area of the prism by its height to get the total volume. In this case, the height is also known, h = 8 cm.
V = b * h = 40 * 8 = 320 cubic cm
Answer:
320
Step-by-step explanation:
The volume of a prism is the height times the area of the base.
V = hA
The base is a triangle. The volume of a triangle is half the base times height.
V = h (½ ab)
Given a = 10, b = 8, and h = 8:
V = ½ (8) (10) (8)
V = 320
Which is the correct solution to the expression 3 + 5 ^ 2? Use the scientific calculator given in this course
Answer:
28
Step-by-step explanation:
Using PEMDAS (or something similar) start off with the exponent.
5^2 would equal 25 since it is multiplying 5 by itself.
Then, you would add 3 to 25 making the answer 28.
For this case we must find the value of the following expression:
[tex]3 + 5 ^ 2 =[/tex]
We have that, replacing in a calculator:
[tex]5 ^ 2 = 5 * 5 = 25[/tex]
Rewriting the expression we have:
[tex]3 + 25 =[/tex]
Equal signs are added and the same sign is placed:
[tex]3 + 25 = 28[/tex]
Answer:
[tex]3 + 5 ^ 2 = 28[/tex]
kyle jogs every 6 days and swims every 4 days. If he jogged and swam today, how many miles until he does both again?
Answer:
12 days
Step-by-step explanation:
Jogging: 6,12,18,24,....
Swimming: 4,8,12,16,20
Looking at the list, the first number in common is 12
The occur together every 12 days
Andrea lost her job as an accountant because her company gave the contract for keeping accounts to a firm in Asia. The company did so to reduce the costs, as it could find cheap labor in the Asian countries. Andrea lost her job due to which type of economic activity? A. recession B. inflation C. outsourcing D. depression E. deflation
When a company looks to have someone outside the company do work it is called out sourcing.
The answer is C.
Answer:
The answer is C.
Step-by-step explanation:
In how many ways can eight people line up from left to right for a group photo
The answer is 8! or 40,320.
8*7*6*5*4*3*2*1=40,320
Answer:
Maybe you might want the long 4 people in the back and the tiny one in the ground just on their knees.(not the begging way)
Also have the tall people give piggy back hold from the tall people for the picture that way it will seen fun.
Step-by-step explanation:
It depends on the theme of the photo if it's painting and fun art or fun time with friends I'd prefer the piggy bag one
If a trip or group photo for a travel I'd pick choice one. It depends believe me there is more thank 5 ways too.
PLZZ I'M IN THE NEED OF BRAINLIST MARK ME PLZZZ!!!
with the current weather conditions a sailboat can sail 5 1/2 miles in an hour.How far can a sailboat sail in 2/3 hours
Answer:
3 2/3 miles
Step-by-step explanation:
distance = rate times time.
Here,
distance = (5.5 mph)(2/3 hr) = 3 2/3 miles
The sailboat can travel 3 2/3 miles in 2/3 hours by multiplying the speed (5 1/2 miles per hour) by the time (2/3 hours) to get the distance.
To determine how far a sailboat can sail in 2/3 hours when it can sail 5 1/2 miles in one hour, we need to perform a multiplication of the speed by the time. The speed of the sailboat is 5 1/2 miles per hour (which is the same as 11/2 miles per hour in improper fraction form), and the time is 2/3 hours.
Here are the steps to calculate the distance:
Convert 5 1/2 miles to an improper fraction: 5 1/2 = (5 times 2 + 1)/2 = 11/2.
Multiply the speed by the time: (11/2) times (2/3) = (11 times 2)/(2 times 3) = 22/6.
Simplify the fraction: 22/6 = 11/3 = 3 2/3 miles.
Therefore, the sailboat can travel 3 2/3 miles in 2/3 hours.
factor the expression and find the zeros h(x)=2x2−11x+15
Answer:
Step-by-step explanation:
(2x-6)(2x-5)
2(x-3)(2x-5)
^ fully factored
x-3=0 2x-5=0
x=3 2x=5
x=5/2
which equation represents the line that passes through the point (1,-5) and has slope of -2? explain and show your work ) A. y= -2x+7 B. y= -2x+11 C. y=-2x-9 D. y= -2x-3
Answer:
D) y = -2x -3
Step-by-step explanation:
1. Create a slope-intercept equation: y = -5, m = -2, x = 1
y = mx + d -> y = -2x + d -> -5 = -2(1) + d
Solve: -5 = -2 + d --> d = -3
So, the y-intercept is -3. Putting that into our equation gives us y = -2x -3
In lowest terms, the ratio 10:4 is written as 5:1. True or False?? I need help IMMEDIATELY
False. It would be 5:2
Explanation
10/2=5
4/2=2
So 5:2
Answer:
No, False
Step-by-step explanation:
10:4 is equal to 10/4, and 5:1 is equal to 5/1.
5:1=5
10:4=2.5
2.5=/=5
if you're standing on the trail 220 feet from the bottom of the tree, you have to look up at a 60 degree angle to see the top . How tall is the tree
Answer:
381.051178
Step-by-step explanation:
222 (tan) 60=381.051178
The height of the tree is 381.05 ft.
Given distance of man from the bottom of the tree is 220 ft.
Let height of the tree be x ft.
Now we have to look up at a 60 degree angle to see the top of the tree.
So we can write in trigonometric ratio form, [tex]tan60= \frac{perpendicular}{base}[/tex]
[tex]\sqrt{3} =\frac{x}{220}[/tex] ( tan 60=[tex]\sqrt{3}[/tex])
[tex]x= 220\times\sqrt{3}[/tex]
[tex]x= 381.05 ft[/tex]
The height of the tree is 381.05 ft.
For more details on trigonometric ratios follow the link:
https://brainly.com/question/1201366
Simplify 2x - 8x - 6y + 9 -14 + x + 11y.
A)5x - 5y - 5
B)-5x + 5y - 5
C)5x + 5y + 5
D)-5x - 5y + 5
B: -5x + 5y - 5
Hope this is the answer you're looking for (:
2x - 8x - 6y + 9 - 14 + x + 11y
-6x + x - 6y + 11y - 5
-5x + 5y - 5
So the answer should be B
Which savings account can a financial institution end?
A.
money market account
B.
youth savings account
C.
credit union account
D.
callable certificate of deposit
Credit union account
The savings account can a financial institution end is callable certificate of deposit. option D
How to determine the accountFinancial institutions have the right to terminate these accounts under certain circumstances, as outlined in their terms and conditions.
Reasons for termination may include customer inactivity, violation of account policies, changes in the institution's product offerings, or regulatory requirements.
Customers should carefully review the account agreements and be aware of any potential fees or penalties associated with account closure.
Learn about savings account at: https://brainly.com/question/30101466
#SPJ6
Help for the two questions shown, please!
Answer:
5) 140.8m^2 6) 360in^2
Step-by-step explanation:
5.
6.4 x 6.4 = 40.96
(7.8 x 6.4) ÷ 2 = 24.96
24.96 x 4 = 99.84
99.84 + 40.96 = 140.8m^2
6.
12 x 10 = 120in
13 x 10 = 130in
5 x 10 = 50in
(12 x 5) ÷ 2 = 30in
30 x 2 = 60in
60 + 50 + 130 + 120 = 360in^2
Laura earns $225 by working 20 hours each week. Write an equation to find how much Laura earns per hour. Use h to represent the hourly rate.
Answer:
20h=225
Step-by-step explanation:
Answer:
20h=225
Step-by-step explanation:
Plz help me with this
Answer: C) 11 + 13 + 15 + 17 + ...
Step-by-step explanation:
[tex]\sum\limits^\infty_3 {2x+5}\\\\2(3) + 5\quad +\quad 2(4) + 5\quad +\quad 2(5)+5\quad +\quad 2(6)+5\quad +...\implies 2(\infty)+5\\\\=11\qquad +\qquad 13\qquad \quad +\qquad 15\qquad \quad +\qquad 17\qquad +...[/tex]
It took Jason 3 minutes and 48 seconds to complete a practice page in class. How many total seconds did Jason take to complete the practice page?
Answer: 228
Step-by-step explanation:
3 X 60 = 180
180 + 48 = 228
For this case we have that by definition, one minute equals 60 seconds. Then, we make the conversion:
[tex]\frac {60 \ s} {1 \ m} * 3 \ m = 180 \ s[/tex]
Thus, 3 minutes equals 180 seconds.
Now:
[tex]180 + 48 = 228[/tex]
So, it took Jason 228 seconds to complete a practice page in class.
Answer:
228 seconds
which point is located at (4, -2, -3)?
point A
point B
point C
point D
I believe it's letter B
Answer:
Point B
Step-by-step explanation:
The graph of f(x) = is shown with g(x). Which equation represents the graph of g(x)? g(x) = g(x) = g(x) = + 1 g(x) = –1
Answer:
B
Step-by-step explanation:
An equation that represents the graph of g(x) include the following: B. [tex]g(x)=\sqrt[3]{x+2}[/tex].
How to determine the transformation (mapping) rule?In Mathematics, a translation is a type of transformation that shifts every point of a geometric object in the same direction on the cartesian coordinate, and for the same distance.
Based on the information provided in the diagram, we have the following:
(x, y) → (x + h, y + k)
(0, 0) → (-2, 0).
-2 = x + h
-2 = 0 + h
h = 0 - 2
h = -2 (2 units left)
0 = y + k
0 = 0 + k
k = 0.
In conclusion, a horizontal translation of 2 units to the left would map the parent cubic function f(x) to the transformed cubic function g(x);
g(x) = f(x + 2)
[tex]g(x)=\sqrt[3]{x+2}[/tex]
Read more on translation here: brainly.com/question/31559256
#SPJ2
Complete Question:
The graph of [tex]f(x) =\sqrt[3]{x}[/tex] is shown with g(x). Which equation represents the graph of g(x)?
[tex]g(x)=\sqrt[3]{x-2} \\\\g(x)=\sqrt[3]{x+2} \\\\g(x)=\sqrt[3]{x} +1\\\\g(x)=\sqrt[3]{x} -1[/tex]
Brainliest to whoever gives the correct answer, no explanation needed
<UST is 30* and I believe <RUS is 30* as well.
Graph Y is less than 1/3 X +1/2
Answer:
Step-by-step explanation:
graph y = 1/3x + 1/2
the slope is 1/3
y intercept is 1/2 ( that would be on the y axis)
slope would be 1/3 . ..up one over three
plot points starting with 1/2 . . and then move the points up one over three
with Y less than that line . . .it would have to move to the right on the number line . . .so you shade the right hand side of the line on the graph
Simplify the product using distributive property 5(x+3) show work
Answer:
Step-by-step explanation:
5(x + 3) Remove the brackets.
5*x + 3*5 Combine
5x + 15
Answer:
[tex]\huge\boxed{\sf{5x+15}}[/tex]
Step-by-step explanation:
Hello.
I hope you remember that the Distributive Property states that
a(b+c)=ab+ac :)
If not, no worries!
Let's simplify this expression:
[tex]\sf{5(x+3)[/tex]
[tex]\sf{5x+15[/tex]
Steps:
I distributed 5 by multiplying it times x and 3 and adding the products.
I hope it helps & have an outstanding day.
[tex]\boxed{imperturbability}[/tex]