Answer:
5
Step-by-step explanation:
We are given the geometric series:
-1, - 2, - 4, - 8.......
In the geometric series above, the common ratio = second term/first term = -2/-1
= 2
Where common ratio is greater than 1(r >1)
The sum of a geometric progression =
Sn = a(rⁿ -1)/r - 1
In the question we are asked to find the number of term = n
Sn = -31
a = -1
r = 2
Hence,
-31 = -1(2ⁿ - 1)/2 - 1
-31 = -1(2ⁿ - 1)
-31 = -2ⁿ + 1
2ⁿ = 1 + 31
2ⁿ = 32
2ⁿ = 2^5
n = 5
Therefore, the number of terms(n) = 5
10500 people visited an art gallery in 2002.This was an increase of 25% on 2001.How many visitors were there in 2001?
Answer:
The amount in 2001 is 8400
Step-by-step explanation:
Let x be the amount in 2001
There is an increase of 25% to get to the amount in 2002
x+ .25x = 1.25 x
1.25x = 10500
Divide each side by 1.25
1.25x / 1.25 = 10500/1.25
x =8400
The amount in 2001 is 8400
Andrew is putting reflective tape around the edge of a stop sign. The sign is a regular octagon, and each side is 11 inches long. How many inches of tape will Andrew need?
Answer:
88 inches
Step-by-step explanation:
We are finding the perimeter of the stop sign, therefor we have to either multiply or add the value of 11. Since this sign is an octagon we will have to multiply by eight or add 11 eight times. This will give you an answer of 88 inches.
Answer:
88 inches
Step-by-step explanation:
The stop sign is in the shape of an octagon. An octogon has 8 sides. If each side is 11 inches you multiply 11 * 8 which is 88.
For what values of the following expressions are true: |a−5|=5−a
Answer:
Whenever a-5<0 or a<5
Step-by-step explanation:
So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450 kilograms ({kg}, but Renna and her load of identical packages mass a total of 620kg. Each package has a mass 37.4kg Write an inequality to determine the number of packages, Renna could remove from the elevator to meet the mass requirement.
Answer:
5 ≤ The number of packages Renna can remove
Step-by-step explanation:
The allowable mass on the elevator is given as 450 kg
The mass of Renna and the packages = 620 kg
The mass of each package = 37.4 kg
The mass Renna should remove from the elevator to meet the mass requirement = 620 - 450 = 170 kg
Therefore, the number of packages, n, Renna should remove can be found from the following inequality
170 ≤ n × 37.4
We note that since the mass of the packages are known, 5 packages weigh 187 kg which is > 170 kg
Therefore, the number of packages to be removed is 170 ≤ n × 37.4 < 187
Dividing by 37.4, we get;
Number of packages to be removed = 4.55 ≤ n < 5 ≈ 5 packages
Given that there whole number packages, we have;
5 ≤ n, which is , 5 ≤ The number of packages Renna can remove.
Answer:
37.4p ≥ 170
Step-by-step explanation:
5 are in total packages.
Trust me this is the answer because I did this before
Hope this helps ;)
An expression is given -6m+9n-12
Answer -3(2m-3n+4)
Step-by-step explanation:
 what is the measure of AC 
Answer:
A
Step-by-step explanation:
The inscribed angle ABC is half the measure of its intercepted arc, thus
arc AB = 2 × 44° = 88° → A
Answer:
A
Step-by-step explanation:
The measure of an inscribed angle is half the measure of it's intercepted arc
Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo's equation is missing, as shown below. Negative (x minus 1) + 5 = 2 (x + 3) minus box
Answer:
The term inside the box should be 3 x.
Step-by-step explanation:
Given the equation:
- (x - 1) + 5 = 2 (x + 3) - T
(where T is the missing term in Leonardo's equation)
we can work with the given terms and accumulate all of them on one side of the equal sign (let's pick the right side for that, and move the tremt T to the left):
- x + 1 + 5 = 2 x + 6 - T
- x + 6 = 2 x + 6 - T
0 = 3 x - T
T = 3 x
For such equation to render infinite number of solutions, the term T on the left must equal "3 x". that way, the equation would be verified for any possible value x.
Answer:
3x
Step-by-step explanation:
i did the test and got it right, hope this helps!
Please help me with this question!
Answer: C) 12.2
================================================
Explanation:
We have a known adjacent side (10) and an unknown hypotenuse (x). The cosine rule ties the two sides together.
cos(angle) = adjacent/hypotenuse
cos(35) = 10/x
x*cos(35) = 10
x = 10/cos(35)
x = 12.2077458876146 approximately
x = 12.2
Make sure your calculator is in degree mode.
Answer:
[tex]\boxed{12.2}[/tex]
Step-by-step explanation:
cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
The hypotenuse of the triangle is x.
cos (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{cos(35)}[/tex]
x = 12.20774588...
x ≈ 12.2
Mr. Duncan bought a table at a discount if 30% thus saving $42. what was the marked price of the table?
Answer:
$140
Step-by-step explanation:
if 30% of full price = $42 then 100% = 42/0.3 = 140
Answer:
$140
Step-by-step explanation:
1. Set up the equation
[tex]\frac{42}{x}[/tex] = [tex]\frac{30}{100}[/tex]
Percentage is out of 100 this equation says 42 of x number is equal to 30%.
2. Cross multiply
30x = 4200
3. Solve for x by dividing both sides by 30
x = 140
What is the measure of angle B in degrees?
119°
Step-by-step explanation:
for this angle A has to be found for that you can use the theorem that states sum of interior angles is equal to the sum of opp exterior angle
51 + A = 112
A = 112 - 51
A = 61°
THEN WE CAN FIND THE B angle
they are angles on a straight line
so 61 + B = 180
B = 119°
Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with respect to the context? The password is weakest if it uses a single symbol for all 7 characters. The strength of the password increases with a decrease in the number of symbols. The password is stronger with an increase in the number of symbols. The password is strongest if a single symbol is used for all 7 characters. There are 2 possible symbol options per character to produce a password of strength of 7 bits. There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Answer:
The password is weakest if it uses a single symbol for all 7 characters.
The strength of password increases with an increase in the number of symbols.
There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Step-by-step explanation:
The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.
Answer:
The three correct options are:
The password is weakest if it uses a single symbol for all 7 characters.
The password is stronger with an increase in the number of symbols.
There are 2 possible symbol options per character to produce a password of strength of 7 bits.
¡Ayuda!
1. Método del Triángulo: Una embarcación navega a una distancia de 800 km hacia el Oeste y después avanza 1400 km a 135 °. ¿Cuál es la magnitud, dirección y sentido del desplazamiento resultante? R /. 2,080 km, 155 ° NO.
Answer:
La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Step-by-step explanation:
En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:
[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]
[tex]r \approx 2045.463\,km[/tex]
La magnitud del desplazamiento resultante es 2045.463 kilómetros.
La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:
[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]
Se despeja el ángulo correspondiente:
[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]
[tex]\alpha \approx 28.945^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es:
[tex]\alpha' = 180^{\circ}-\alpha[/tex]
[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]
[tex]\alpha' = 151.055^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Which function is graphed below?
Answer:
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Step-by-step explanation:
The graph represents a second order polynomial function (a parabola), whose axis of symmetry is the x-axis and whose form is presented as follows:
[tex]x - h = C\cdot (y-k)^{2}[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Dependent and independent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless. If [tex]C > 0[/tex], then vertex is an absolute minimum, otherwise it is an absolute maximum.
After a quick observation, the following conclusions are done:
1) Vertex is an absolute minimum ([tex]C > 0[/tex]) and located at (-2, 0).
2) Parabola pass through (2, 2).
Then, the value of the vertex constant is obtained after replacing all known values on expression prior algebraic handling: ([tex]x = 2[/tex], [tex]y = 2[/tex], [tex]h = -2[/tex], [tex]k = 0[/tex])
[tex]2+2 = C\cdot (2-0)^{2}[/tex]
[tex]4 = 4\cdot C[/tex]
[tex]C = 1[/tex]
The function is:
[tex]x = -2 + 1\cdot y^{2}[/tex]
[tex]x = y^{2}-2[/tex]
The inverse function of this expression is [tex]y = \pm \sqrt{x+2}[/tex]
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Anjana is riding a motorboat at Katara starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s^2 for 8 s. How far does she ride the boat during this time?
Answer:
96 meters
Step-by-step explanation:
The computation of the distance far from her ride the boat during this time is shown below:
According to the kinematics motion equation
[tex]s = u \times t + \frac{1}{2} \times a \times t^{2}[/tex]
where,
o = 0 m/sec
a = 3.0 m/sec
t = 8.0 sec
Now placing these values to the above formula
So, the distance far from her ride is
[tex]= 0 \times 8 + \frac{1}{2} \times 3 \times 8^{2}[/tex]
= 96 meters
We simply applied the above formula
3. The diagram shows a piece of rectangular tile
PQRS. A kite shape TUVW is inscribed in the
rectangle. Given that the perimeter of PQRS is
120 cm, find the area of TUVW.
Answer:
432cm²
Step-by-step explanation:
If the Perimeter is 120cm, PT=8 (120-28-12-12-28-12-12)/2
This means the rectangle is 24x36.
area of a kite is the diagonals divided by 2 (or half of the rectangle).
24x36=864
864/2=
432 cm²
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Answer:
a. (True) Since ∠6 and ∠8 are vertical angles, they are congruent.
b. (False) ∠1 and ∠2 are supplementary but 65 + 125 ≠ 190.
c. True
d. True
e. True
Answer:
The answer is Freddy Kruger
Step-by-step explanation:
Elm Street, duh
Find the value of z.
Answer:
2
Step-by-step explanation:
opposite angles are the same
the shape opposite to 'z' is labelled with 2
which means that, that angle is 2 degrees
which also means that z would be 2 aswell.
The supply and demand curves for a product line of bicydes are shown. A protimately where is the equilibrium pointe
у
350
Quantity
300
+250
+200
+150
+100
demand
+50
20
80 100 120 140 160 180 200 220 240 250 200 300
Price (dollars)
A (93,268)
B. (132,220)
C.(180,355)
D.(220,115)
Answer:
It's B
Step-by-step explanation:
plato
to solve the equation 3 x + 1 = 4 x + (negative 4)
Answer:
x=5
Step-by-step explanation:
3x+1 = 4x -4
Subtract 3x from each side
3x+1-3x = 4x-3x-4
1 = x-4
add 4 to each side
1+4 = x-4+4
5 =x
Answer: x=5
Step-by-step explanation:
3x+1=4x+(-4)
3x+1=4x-4
3x+5=4x
5=x
Rewrite the following radical expression in rational exponent form.
Answer:
[tex]x^\frac{3}{7}[/tex]
Step-by-step explanation:
we can write [tex]\sqrt[7]{x}[/tex] as [tex]x^\dfrac{1}{7}[/tex] and we multiply 1 by 3 to get [tex]x^\frac{3}{7}[/tex]
Evaluate each expression for the given values of the variables: |a+x|/2-|a-x|/2if a=−2; x=−6
Answer:
2
Step-by-step explanation:
|a+x|/2-|a-x|/2
Plug in the values.
|-2+-6|/2-|-2- -6|/2
Evaluate.
|-8|/2-|4|/2
Apply rule : |-a| = a
8/2 - 4/2
4 - 2
Subtract.
= 2
Please help ASAP. The question is down below. Thanks
Answer:
B
Step-by-step explanation:
there is three sections to be fenced using 78 m of fence so it would be letter B.
Which point is on the line that passes through point R and is perpendicular to line PQ? (–6, 10) (–4, –8) (0, –1) (2, 4)
Answer:
(-4, -8)
Step-by-step explanation:
Let the coordinates of common point of the given lines are (x, y),
Thus, the slope of the line passes through the points (a, b) and R(4,2) is,
2 - b
m1 = ------
4 - a
Again, the slope of the line passes through two points P(-6,4) and Q(4,-4),
-4 - 4 -8 -8 -4
m2 = ------ = --------- = --------- = ---------
4- (-6) 4 + 6 10 5
= m1 * m2 = -1
2 - b -4
= ------- x ---- = -1
4 - a 5
8 - 4b
= ----------- = 1
20 - 5a
= 8 - 4b = 20 - 5a
= 5a - 4b = 12 --------- equation 1
For a = -6 and b = -10
5 x -6 - 4 x 10 = -70 ≠ 12
For a = -4 and b = -8
5 x -4 - 4 x - 8 = 12 = 12
For a = 0 and b = -1
5 x 0 - 4 x -1 = 4 ≠ 12
For a = 2 and b = 4
5 x 2 - 4 x 4 = -6 ≠ 12
therefore Second is correct
hope it helps and i get the brainliest.
The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.
What is the equation of a perpendicular line?If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The points are P(-6, 4), Q(4, -4), and R(4, 2). Then the slope of the line PQ is calculated as,
m = (4 + 4) / (-6 - 4)
m = - 4/5
The slope of the perpendicular line is calculated as,
⇒ -1/m
⇒ -1/(-4/5)
⇒ 5/4
The equation of the perpendicular line is written as,
y - 2 = (5/4)(x - 4)
y - 2 = (5/4)x - 5
y = (5/4)x - 3
Let's check which option satisfies the equation. Then we have
a) For, x = -6 and y = 10, then we have
10 = (5/4) (-6) - 3
10 ≠ - 10.5
b) For, x = -4 and y = -8,
-8 = (5/4) (-4) - 3
-8 = -8
c) For, x = 0 and y = -1,
-1 = (5/4) (0) - 3
-1 ≠ - 3
d) For, x = 2 and y = 4,
4 = (5/4) (2) - 3
4 ≠ - 0.5
The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.
More about the equation of a perpendicular line link is given below.
https://brainly.com/question/14200719
#SPJ7
Analyze the diagram below and complete the instructions that follow.
Find the value of M angle 2 + M angle 4
Answer:
200°
Step-by-step explanation:
<2 = 90° (right angle)
<3 = 70° (vertically opposite angles)
<4 + <3 = 180° ( angles on a straight line)
<4 + 70 = 180°
<4 = 180° - 70°
<4 = 110°
<2 + < 4
= 90 ° + 110° = 200°
Please help!! Don't anwser if you dont know it :) Brainliest for right anwser
Answer:
D. The graph of g(x) is horizontal stretched by a factor of 3.
Step-by-step explanation:
Multiplying x by 1/3 stretches the graph horizontally by a factor of 3.
Answer:i think its d too
Step-by-step explanation:
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground.
Answer:
The bird is 2.44km high
Step-by-step explanation:
Hello,
To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.
See attached document for better understanding.
From the first diagram, we understand that the bird is between them and also on top of them.
Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.
But before then, we should know that sum of angles in a triangle is equal to 180°
Therefore,
20° + 50° + b° = 180
70° + b = 180
b = 180° - 70°
b = 110°
Dividing angle b into two equal parts = 55° on each side.
See the last attached document for better illustration.
Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.
We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.
Tanθ = opposite / adjacent
Tan 55° = 3.5 / adj
Adjacent = 3.5 / tan55
Adjacent = 3.5 / 1.43
Adjacent = 2.44km
The height of the bird is 2.44km
Answer:
A. 1.95
Step-by-step explanation:
PLATO
plzzzz answer right away will mark BRAINLIST AND FIVE STARS PLUS THANKS What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFraction StartFraction 8 over 9 EndFraction 1
Answer:
Proportionality Constant = k = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Equation is:
[tex]y = \frac{x}{9}[/tex]
=> [tex]y = (\frac{1}{9} ) x[/tex]
Comparing it with [tex]y = kx[/tex], where k is the proportionality constant, We get:
Proportionality Constant = k = [tex]\frac{1}{9}[/tex]
Answer:
[tex]{\sf \frac{1}{9}}[/tex]
Step-by-step explanation:
y and x are the directly proportional quantities.
[tex]\sf y=kx[/tex]
The constant of proportionality is k.
The equation is:
[tex]\sf y=\frac{x}{9}[/tex]
[tex]\sf y=\frac{1}{9} x[/tex]
The value of k in this equation is:
[tex]\sf k= \frac{1}{9}[/tex]
Find the radius of a circle that has an arc whose central angle measures 17 degrees and has a length of 12 degrees.
Answer:
The radius of the circle is 40.44 cm
Step-by-step explanation:
We can use the formula for the arc of a circle of radius R and central angle [tex]\theta[/tex], where [tex]\theta[/tex] is given in radians (we therefore convert [tex]17^o[/tex] into radians with [tex]17^o\,\pi/180^o=0.2967[/tex] radians)
[tex]arc=R\,\theta\\12\,cm= R\,\theta\\12\,cm=R\,(0.2967)\\R=\frac{12}{0.2967} \,cm\\R=40.44\,cm[/tex]
Can you help me it’s algebra 2 and I need the answers for like 5 more questions, it’s urgent like really urgent!!!!
Answer: B) as x → -5 from the left, y → -∞
as x → -5 from the right, y → +∞
Step-by-step explanation:
[tex]g(x) =\dfrac{x^2+15x+56}{x+5}\quad =\dfrac{(x+7)(x+8)}{x+5}\\\\\\\text{Evaluate from the left. Let x = -6}\rightarrow \dfrac{(-)(-)}{(-)}=-\\\\\\\text{Evaluate from the right. Let x = -4}\rightarrow \dfrac{(-)(-)}{(+)}=+[/tex]
Refer to the graph which confirms that
from the left, y tends toward -∞from the right, y tends toward + ∞10
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y=-3x + 7
X
у
х
y
0
5
-6
9
3
6
-3
8
6
7.
0
7
9
8
3
6
The equation that represents the other equation is y =
X+ .
The solution of the system is (
Reset
Next
Answer: The equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .
The solution of the system is (3,6).
Step-by-step explanation:
Linear equation: [tex]y=mx+c[/tex] , where m= slope
c = y-intercept.
In the first table, the y-intercept = 5 [ y-intercept = value of y at x=0.
Slope for first table = [tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}[/tex]
The equation that represents the first table:
[tex]y=\dfrac{1}{3}x+5[/tex]
So, the equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .
Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.
Here, x=3 and y=6 is the common value in both tables.
So, the solution of the system is (3,6).
The linear equation of the first table is y = 1 / 3 x + 5
The solution to the system of equation is (3, 6)
Point slope equation;y = mx + bwhere
m = slope
b = y-intercept
Therefore, y = - 1 /3 x + 7 is the equation for the second table.
The equation for the first table can be solved using (0, 5)(3, 6) from the table. Therefore,
m = 6 - 5 / 3 - 0 = 1 / 3
let's find b using (0, 5)
5 = 1 / 3(0) + b
b = 5
Therefore, the equation of the first table is as follows:
y = 1 / 3 x + 5The solution to the system of equation can be calculated as follows:
y + 1 /3 x = 7
y - 1 / 3 x = 5
2y = 12
y = 12 / 2
y = 6
6 - 1 / 3 x = 5
- 1 / 3 x = 5 - 6
- 1 / 3 x = - 1
x = 3
Therefore, the solution to the system of equation is (3, 6)
learn more on linear equation here: https://brainly.com/question/2263981?referrer=searchResults