Step-by-step explanation:
We write that x belongs to the interval if a ≤ x ≤ b. Graphically, a closed interval is represented by a segment whose two ends are filled. To write this interval in interval notation, you must use square brackets: [a,b].
Solve for x. Round to the nearest tenth, if necessary.
find the 9th and 15th terms of the following geometric sequence 2, -4, 8, -16
Step-by-step explanation:
given the geometric sequence 2, -4, 8, -16, ...
a1 = 2
r = -4/2 = -2
find : a9 and a15
solutions:
an = a1. r^(n-1)
=> a9 = 2. (-2)^(9-1)
= 2. (-2)^8
= 2. 2^8
= 2^9
= 512.
=> a15 = 2. (-2)^(15-1)
= 2. (-2)^14
= 2. 2^14
= 2^15
= 32,768
Step-by-step explanation:
Hey there!
The given geometric sequence is: 2, -4, 8, -16.
The;
a1 = 2
Common ratio (r) = T2/T1
= -4/2
= -2
Now;
Use general formula of geometric sequence;
[tex]tn = {a1.r}^{n - 1} [/tex]
Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.
Then;
[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]
or, t9 = 2*256
Therefore, t9 = 512.
Again;
[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]
or, t15= 2*16384
Therefore, t15 = 32768.
Hope it helps!
The pie chart shows how 36 pupils travel to school.
Use the pie chart to complete the table.
Bike
Walk
Travel to
school
Number
of pupils
Walk
9
120°
Car
Bus
Bus
Car
Bike
Total
36
Answer:
[tex]Bike = 7[/tex]
[tex]Car = 8[/tex]
[tex]Walk = 9[/tex]
[tex]Bus = 12[/tex]
Step-by-step explanation:
Given
[tex]Bus = 120^o[/tex]
[tex]Walk = 90^o[/tex]
[tex]Car = 80^o[/tex]
[tex]n = 36[/tex] --- pupils
Required
Determine the number of students in each category
This is calculated by dividing the measure of each category by 360; then multiply the result by the number of pupils:
So, we have:
[tex]Bus = \frac{120}{360} * 36 = \frac{1}{3} * 36 = 12[/tex]
[tex]Walk = \frac{90}{360} * 36= \frac{1}{4} * 36 = 9[/tex]
[tex]Car = \frac{80}{360} * 36 = \frac{80}{10} = 8[/tex]
To calculate the number of students that travel by bike, we have:
[tex]Car + Bike + Walk + Bus= n[/tex]
Substitute values
[tex]8 + Bike + 9+ 12= 36[/tex]
Collect like terms
[tex]Bike = 36 - 8 - 9 - 12[/tex]
[tex]Bike = 7[/tex]
Answer:
Look at picture
Step-by-step explanation:
The function s(t) = t2+2t+5shows the height s(t), in feet, of a water balloon after t seconds. A second water balloon moves in the air along a path represented by p(t)=11+3t where p(t) is the height, in feet, of the balloon from the ground at time t seconds
Part A: Create a table using integers 1 through 4 for the two functions. What is the solution for s(t) = p(t)? How do you know? Include the table in your answer.
Part B: Explain what the solution from Part A means in context of the problem.
Answer:
t =2 , 3
Step-by-step explanation:
s (t) = t^2 + 2 t + 5
p (t) = 11 + 3 t
(a) s (1) = 8
s (2) = 13
s (3) = 20
s (4) = 29
p (1) = 14
p (2) = 17
p (3) = 20
p (4) = 23
Now equate both of them
[tex]t^2 + 2t + 5 = 11 + 3 t \\\\t^2 - t - 6 =0 \\\\t^2 - 3 t + 2t - 6 =0\\\\t(t - 3) + 2 (t - 3) = 0\\\\(t -3)(t-2)=0\\\\t =3, 2[/tex]
(b) It shows that the values are same at = 2 and t = 3.
h(x) = x2 + 3. Is frl a function and why/why not?
No, the inverse function does not pass the horizontal line test.
No, the inverse function does not pass the vertical line test.
Yes, the inverse function has one y-value for every x-value.
Yes, the inverse function has one x-value for every y-value.
is good answer the x value and y value
Answer:
No, the inverse function does not pass the horizontal line test.
Step-by-step explanation:
Miguel's scores on his first three math
PACE Tests were 95, 92, and 90. What
score does he need on his next test to
have a 94 average?
Answer: 99
Step-by-step explanation:
Fourth PACE Test = xSince the average of all four tests is 94:
[tex]\frac{95+92+90+x}{4} =94\\\\(4)\frac{277+x}{4} =(4)94\\\\277+x=376\\\\x=376-277=99[/tex]
with steps please
A student uses a clinometer to measure the angle of elevation of a sign that marks the point on a tower that is 45 m above the ground. The angle of elevation is 32° and the student holds the clinometer 1.3 m above the ground. He then measures the angle of elevation of the top of the tower as 47º. Sketch and label a diagram to represent the information in the problem. Determine the height of the tower to the nearest tenth of a metre
Answer: [tex]75\ m[/tex]
Step-by-step explanation:
Given
The tower is 45 m high and Clinometer is set at 1.3 m above the ground
From the figure, we can write
[tex]\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m[/tex]
Similarly, for [tex]\triangle ACD[/tex]
[tex]\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m[/tex]
Height of the tower is [tex]43.7+31.29\approx 75\ m[/tex]
Find the length of AC. Round to the nearest hundredth if necessary.
Answer:
13.86
Step-by-step explanation:
In ∆ ABC ,
cos 30° = AC/BC√3/2 = AC/ 16 AC = 16 * √3/2 AC = 8√3 AC = 8 * 1.732AC = 13.86Type the correct answer in each box.
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was
2
times the weight of the first fish, another was
2
more than
3
times the weight of the first fish, the next was
1
2
the weight of the first fish, and the last was
3
5
the weight of the first fish.
Bridget’s dad caught four fish. The first fish he caught weighed
2
more than
3
times the weight of the first fish caught that day.
One fish weighed
4
5
the weight of the first fish caught that day, one weighed
4
more than
2
times the weight of the first fish caught that day, and the last weighed
1
2
the weight of the first fish caught that day.
Answer:
PLZZ MARK ME BRAINLIEST..!
Step-by-step explanation:
Bridgets fish: f , 2f, 3f+2 , 1/2f, 3/5f
Add for total weight: 7 1/10 f +2
Dads fish: 3f+2, 4/5f, 2f+4, 1/2f
Add for total weight: 6 3/10f +6
set the 2 total weights equal:
6 3/10f +6 = 7 1/10f +2
Subtract 6 3/10f from each side:
6 = 8/10f + 2
Subtract 2 from each side:
4 = 8/10f
Divide both sides by 8/10:
f = 5
Bridget's first fish weighed 5 ounces.
Dads first fish weighed: 2 more than 3 times :3(5) + 2 = 15 +2 = 17 ounces.
What is the vertex of
y= 3/4x^2+3x+2
Answer:
The vertex is located at (-2,-1)
Step-by-step explanation:
Let a and b be the solutions to x^2 + x − 3 = 0. Find the value of a^3 − 4b^2 + 19.
If you can't solve it don't answer.
This is a challenge.
Good luck!
Answer:
0.037
Step-by-step explanation:
Given that,
Let a and b be the solutions to [tex]x^2 + x -3 = 0[/tex]
It can be solved using quadratic formula where a = 1, b = 1 and c = -3
So,
[tex]x=\dfrac{-1+\sqrt{1^2-4\times 1\times (-3)}}{2(1)},\dfrac{-1-\sqrt{1^2-4\times 1\times (-3)}}{2(1)}\\\\x=1.30,-2.3[/tex]
Let a = 1.3, b = -2.3
The value of [tex]a^3 -4b^2 + 19[/tex] can be given by :
[tex]a^3 -4b^2 + 19=(1.3)^3-4\times (-2.3)^2+19\\\\=0.037[/tex]
So, the value of the given expression is 0.037.
For each square there are 3 circles. Which model shows this relationship?
ОО
Answer:
The one in the middle 100% correct
Answer:
second option
Step-by-step explanation:
Ratio of square to circle = 1 : 3
In the second option:
Square = 2 & circles = 6
Ratio = 2 : 6 and after simplifying, Ratio = 1 : 3
What are the side of triangle PQR
how do you solve 2x+320=425
Answer:
how to solve your problem
Step-by-step explanation:
2x320=425
subtract both 320 both from sides of the equation
2x+320-320=425-320
subtract numbers
2x=105
divide both sides of equation by the same terms
2x/2=105/2
simplify
x=105/2
answer is x=105/2
Helen drives 195miles in 3 hours
what is her average speed in mph
Answer:
65 mph is the correct answer
Answer:
s=d/t
=195/3
=65 mph
Given the net of the rectangular prism, what is its surface area?
Answer:
D. 160
Step-by-step explanation:
solve the equation
45 = 3(x + 1)
Answer:
x = 14
Step-by-step explanation:
45 = 3(x + 1)
Distribute the 3
3(x) = 3x
3(1) = 3
We now have 45 = 3x + 3
Subtract 3 from both sides
45 - 3 = 42
3 - 3 cancels out
We now have 42 = 3x
Divide both sides by 3
42/3 = 14
3x / 3 = x
We're left with x = 14
Answer:
x = 14
Step-by-step explanation:
45 = 3(x + 1)
Distribute
45 = 3x + 3
-3 -3
----------------
42 = 3x
---- ----
3 3
14 = x
Suppose you own a rowboat and sometimes go rowing in the summer. In June, you are planning to go rowing with two of your friends (three people total in the boat), and in July, you are planning to go rowing with just one friend (two people total in the boat). Will you put in more effort (row harder) on the three-person trip or on the two-person trip?
Answer:
The three-person trip require more effort (row harder) than the two person-trip
Step-by-step explanation:
The number of persons in the boat determines the mass of the boat
The mass of the boat with three people in total is more than the mass of the boat with only two person's
Mass is a measure of inertia, which is the resistance of a body to accelerate, and therefore, to the application of a force
Therefore, on the three-person trip were three people are in the boat, the boat has more mass, and therefore more inertia and will require more effort (force) than on the two-person trip that has a lesser mass
solve the following problems
The Law of Sines: Mastery Test ? In triangle ABC, how long is side a if A = 24°, C = 55°, and c = 3? O 1.49 O 1.31 O 6.04 O 0.1
Answer:
Step-by-step explanation:
Using the Law of Sines, our proportion would be
[tex]\frac{sin24}{a}= \frac{sin55}{3}[/tex] and cross multiply to get
3sin24 = asin55 and solve for a:
[tex]a=\frac{3sin24}{sin55}[/tex] so
a = 1.49, the first choice.
geometrical representation of (a+b)2and (a-b)2
Step-by-step explanation:
hope this will help you if it really help you mark me as brinalist friend please
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
14
x
х
12
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are acute, obtuse, isosceles, equilateral, scalene and right angled triangle.
A right angled triangle is a triangle in which one of the angles is 90°. In a right angled triangle, the longest side is known as the hypotenuse and the side is opposite to the right angle.
Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given the question attached, using Pythagoras theorem:
18² = x² + 12²
324 = x² + 144
x² = 180
x = 13.42
[tex]\text{Solve for x.}\\\\5x + 10 = 35[/tex]
Answer:
x = 5
Step-by-step explanation:
5x + 10 = 35
Subtract 10 from both sides
5x + (10-10) = 35 - 10
Simplify
5x = 25
Divide both sides by 5
5x/5 = x
25/5 = 5
We're left with x = 5
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{x = 5}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'....}}\\\\5x + 10 = 35\\-------------\\\rightarrow 5x + 10 - 10 = 35 - 10\\\\\rightarrow 5x = 25\\\\\rightarrow \frac{5x=25}{5}\\\\\rightarrow \boxed{x = 5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
what’s the answer? how do I solve this?
Answer:
39.96 is what I think is the answer :)
The angle of elevation of a tree at a distance of 10m from the foot of the tree is 43°. Find the height of the tree
Answer:
9.32m is the height of. the tree from the ground.
Helppppp and explain pls and thankyouuu
Answer: B
Step-by-step explanation:
multiply all the the sales by 11% and you will get the answers in option b
ex: 1300*0.11=143
The graph of a line goes down and to the right when:
A. there is no coefficient of x.
B. the coefficient of x is 0.
c. the coefficient of xis positive.
D. the coefficient of x is negative.
Answer:
The answer is D.
Step-by-step explanation:
When a graph of a line goes down and to the right, it shows that as the value of x increases, the value of y decreases. This represents a negative coefficient for x.
The graph is a drawn out version of the question.
Te graph of a line goes down and to the right when the coefficient of x is negative, option (D) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
y = mx + c
We have:
The graph of a line goes down and to the right when.
The orientation of the line depends on the slope.
If the slope of the line is positive, the line will go up.
If the slop of the line is negative, the line will go down.
Thus, the graph of a line goes down and to the right when the coefficient of x is negative, option (D) is correct.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
can someone please help me solve this? thank you!:)
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
Juan compró un led TV en cuotas que costó $ 76.000=. Si le falta pagar 3 cuotas y ya pagó $ 47.000, ¿Cuál es el valor de cada cuota fija?
Respuesta:
$ 9666. 67
Explicación paso a paso:
Costo de TV = $ 76,000
Número de cuotas = 3
Monto ya pagado = $ 47000
Amontof cada cuota fija = Cantidad que queda por pagar / 3
Cantidad que queda por pagar = Costo de TV - Cantidad ya pagada
Cantidad que queda por pagar = $ (76000 - 47000) = $ 29000
Monto de cada cuota fija = $ 29000/3 = $ 9666. 67
What single decimal multiplier would
you use to increase by 9% followed by
6% decrease?
Answer:
1.0246
Step-by-step explanation:
100*1.09 = 109
109*0.94 = 102.46
102.46% = 1.0246
