Anna and Sam each want to run for president of their school's student body council. In order
to do so, they must collect a certain number of signatures and get a nomination. So far, Anna
has 20 signatures, and Sam has 25. Anna is collecting signatures at an average rate of 6 per
day, whereas Sam is averaging 5 signatures every day. Assuming that their rate of collection
stays the same, eventually the two will have collected the same number of signatures. How
long will that take?
Time
elapsed
Write a system of equations, graph them, and type the solution.
Answers
Answer:
6x+20=5x+25
5 days
Step-by-step explanation:
Let x = the days that they have the same amount of signatures
We know Anna has 20 currently and gets 6 per day, so we can use y=mx+b to describe her linear relationship.
We also know that Sam has 25 and gets 5 per day, so we can again use y=mx+b to describe his linear relationship.
Since both equations equal the variable y, we can say they equal each other and set up 6x+20=5x+25.
Then you subtract 20 from both sides and subtract 5x, so you are left with x =5, or 5 days until they have the same amount of signatures
Hope this made sense :D
Related Questions
find the midpoint of the line segment joining the two points (-1,-1) and (-5,4)
Answers
Answer:
(-3, 1.5)
Step-by-step explanation:
equation: M = (x1+x2)/2 , (y1+y2)/2
So, plug it in.
(-1-5)/2 , (-1+4)/2
-3 , 1.5
so, x = -3 and y = 1.5
Two ships leave a harbor together traveling
on courses that have an angle of 128°
between them. If they each travel 543 miles,
how far apart are they (to the nearest mile)?
A) 976 mi
B) 476 mi
C) 42 mi
D) 1952 mi
Answers
Answer:
use cosine law
x^2 = 543^2 + 543^2 - 2(543)(543cos 128°
solve for x
Step-by-step explanation:
Find f(2) and f(3).
f(1) = 3
f(n) = 7f(n = 1)
Answers
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
A number more than 1.
Answers
Answer:
there is no more number than one
Step-by-step explanation:
EASY QUESTION! MARK BRAINLIEST!
if i pay $3.50 a month how much do i pay a year? :)))
Answers
Answer:
42
Step-by-step explanation:
3.50x12 = 42
9. GIVEN: y(x + 1) = 51; y = 3 PROVE: x = 16
Answers
Answer:
see explanation
Step-by-step explanation:
y(x + 1) = 51 ← substitute y = 3 into the equation
3(x + 1) = 51 ( divide both sides by 3 )
x + 1 = 17 ( subtract 1 from both sides )
x = 16
Given:
y(x + 1) = 51y = 3What to prove: x = 16
=> y(x + 1) = 51=> 3(x + 1) = 51=> 3x + 3 = 51=> 3x = 51 - 3=> 3x = 48=> x = 16Conclusion:We have now proved that x = 16.
Hoped this helped.
[tex]BrainiacUSer1357[/tex]
Find the inverse function. f(x) = Vx - 1+4
Answers
Answer:
f^-1(v)=v/x-3/x
Step-by-step explanation:
The inverse of the function f(x) = [tex]\sqrt[3]{x-1} + 4[/tex] Is f⁻¹(x) = (x - 4)³ + 1.
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
f(x) = [tex]\sqrt[3]{x-1} + 4[/tex]
y = [tex]\sqrt[3]{x-1} + 4[/tex]
Calculate the inverse of the function as shown below,
Replace x with y,
x = [tex]\sqrt[3]{y-1} + 4[/tex]
x - 4 = [tex]\sqrt[3]{y- 1}[/tex]
Cube both sides,
(x - 4)³ = y - 1
y = (x - 4)³ + 1
Thus, f⁻¹(x) = (x - 4)³ + 1
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Calculate the volume of a regular octahedron whose edges are all 10 cm (do not use the formula to find the volume)
Answers
Answer:
V≈471.4cm³
Step-by-step explanation:
V =
[tex] \frac{1}{3} \times \sqrt{2} \times {a}^{3} [/tex]
V= 471.4
Answer:
Solution :Here we have given that the all edges if octahedron are 10 cm. We need to find the volume of regular octahedron.
[tex] \rule{300}{1.5}[/tex]
As we know that the formula of volume of octahedron is :
[tex]\longrightarrow{\pmb{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]
Substituting all the given values in the formula to find the volume of regular octahedron :
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10)}^{3}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10 \times 10 \times 10)}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(1000)}}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{ \sqrt{2} }{3} \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = 0.471404 \times 1000}}}[/tex]
[tex]{\longrightarrow{\sf{\underline{\underline{\red{Volume_{(Octahedron)} \approx 471.404 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of regular octahedron is 471.404 cm³.
[tex] \rule{300}{1.5}[/tex]
f the family decides to fly, they know that they will need a rental car for at least part of their trip. Gabriela and Luis estimate a budget of $315
$
315
for rental car expenses. One rental car company charges $55
$
55
per day and $35
$
35
in taxes and fees. They also estimate that they will spend $15
$
15
per day on gas. Gabriela wrote the equation (55d+35)+15d=315
(
55
d
+
35
)
+
15
d
=
315
to determine the number of days the family can rent a car from this company.
How many days could the Morales family rent a car if they choose this rental car company with their estimated budget?
Answers
Answer:
4 days
Step-by-step explanation:
55d+35+15d=315
70d=315-35
70d=280
d=280/70
d=4
46. A sphere shaped bowl has a radius of 5.5 inches How much water can the bowl hold? Round to the nearest tenth.
Answers
Answer:
try 17.89 cm..then 18 for answer
Please Help Question in picture
Answers
Answer:
(-3, 5.5)
Step-by-step explanation:
To find the midpoint, you add up the corresponding coordinates (x with x and y with y) and divide each by 2.
(-7+1)/2 = -3
(8+3)/2 = 5.5
Answer:
(-3,5.5)
Step-by-step explanation:
(-7,8)
(1,3)
(-7+1)/2,(8+3)/2
-3,5.5
Please help!
Can someone write out an explanation for how to simplify:
[tex](4x^{-4} )^{-3}[/tex]
I'm having trouble understanding it so a step by step would be helpful!
Answers
(4 • 1/x^4)^-3
Next, multiply the terms in the parentheses.
(4/x^4)^-3
Express ^-3 as a positive exponent by finding the reciprocal of the fraction inside the parenthesis.
(x^4/4)^3
Then, distribute the power into the parentheses. (Numerator and denominator)
x^12/64
Hope this helps!
3
3
3
3
3
I pentagon
2 pentagons
3 pentagons
Represent the relationship using a table. Complete the table below.
Number of Perimeter,
Pentagons, X
1
Ordered
Pair (x,y)
2
3
(Simplify your answers.
Answers
The relationship between the number of pentagons and the perimeter will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
From the diagram in the question, each side of a pentagon has length [tex]3units[/tex].
Also, each time another pentagon is attached, a side is removed.
Using these observations, we can create a relationship between the number of pentagons, [tex]x[/tex], and the perimeter, [tex]y[/tex], as follows
For [tex]x=\text{number of sides}=1[/tex]
[tex]y=\text{perimeter}=3\times 5=15units[/tex]
For [tex]x=2[/tex]
[tex]y=3\times5+3\times5-1\\=15+15-1\\=29units[/tex]
For [tex]x=3[/tex]
[tex]y=3\times5+3\times5-1+3\times5-1\\=3\times5+3\times5+3\times5-1-1\\=15+15+15-2=43units[/tex]
The relationship will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
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Paul has 0.50$ in his pocket. What fraction of a dollar does he have
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
Paul has 1/2 of a dollar.
Step-by-step explanation:
A haft of a dollar is 50 cents since 1 dollar is 100 cents so the fraction simplified would be 1/2 or 50/100.
pls help (written response pls)
Answers
Answer:
It would be Number of Hours
Step-by-step explanation:
The word Dependent Variable means a number/something that relies on something else so the word "Number" Relies and something to follow it up and in this sentence it's "number of hours"
Hope this Helps :)
How many different types of triangles are there?
Draw and name the 4 different triangles.
Write the properties of each triangle.
Draw a circle and name the different parts of the circle.
Find the relationship between radius and diameter.
NO SPAM!
Answers
Answer:
Explanation :How many different types of triangles are there?
There are 6 types of triangles.
➝ Scalene Triangle➝ Isosceles Triangle➝ Equilateral Triangle➝ Acute Triangle➝ Obtuse Triangle➝ Right Triangle[tex]\begin{gathered}\end{gathered}[/tex]
Draw and name the 4 different triangles.
[tex]\green\implies[/tex] The diagram of 4 different triangles is in the given pic. So, please check out the attachment.
The name of four triangles are :
➝ Right angled triangle ➝ Isosceles triangle ➝ Equilateral triangle ➝ Scalene triangle[tex]\begin{gathered}\end{gathered}[/tex]
Write the properties of each triangle.
1. Acute-angled Triangle
[tex]\pink\implies[/tex] Each of the angles is below 90⁰, and the sum of those angles is always 180⁰.
2. Right-angled Triangle
[tex]\pink\implies[/tex] One side being 90⁰, the other angles have to be acute. It is because the addition of all internal angles always produce 180⁰.
3. Obtuse-angled Triangle
[tex]\pink\implies[/tex] Naturally, the other two angles have to be smaller than an obtuse angle. It is so that the internal sum of all the angles remains 180⁰.
4. Equilateral Triangle
[tex]\pink\implies[/tex] Since the internal angles add up to 180⁰, each angle has to be equal in an equilateral triangle. In this case, each angle of this triangle is 60⁰.
5. Isosceles Triangle
[tex]\pink\implies[/tex] Since two sides have the same length, the third side has to have a different length. On top of that, the angle of the other side is also dissimilar to the previous angles.
6. Scalene Triangle
[tex]\pink\implies[/tex] In this case, the lengths of the three sides are diverse. However, the sum of dissimilar internal angles also has to be 180⁰.
[tex]\begin{gathered}\end{gathered}[/tex]
Draw a circle and name the different parts of the circle.
[tex]\green\implies[/tex] The diagram of circle is in the given pic. So, please check out the attachment.
Parts of circle :
A circle can have different parts and based on the position and shape, these can be named as follows:
➝ Centre➝ Radius➝ Diameter➝ Circumference➝ Tangent➝ Secant➝ Chord ➝ Arc➝ Segment➝ Sector[tex]\begin{gathered}\end{gathered}[/tex]
Find the relationship between radius and diameter.
[tex]\pink\implies[/tex] The relationship between radius and diameter is the diameter of a circle is twice of its radius.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
There are 25 students in Mr. Detwikers 1st period class. If 76% of these students complete their homework last night. How many students did their homework?
Answers
Mattie Evans drove 160 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.
Answers
Answer:
Step-by-step explanation:
The speed of the plane was 291.13mph.
What is speed?Speed is distance travelled per unit time. It is scalar quantity
Given
The difference in distances was 600 miles; the difference in speeds was 190mph. That means the time was 600/190 = 3.16 hours.
Since the plane flew 920 miles in that time, its speed was 920/3.16 = 291.13mph.
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Jenny received a $30.50 gift card for a photo center. She used it to buy prints that cost 20 cents each. The remaining balance, B (in dollars), on the card after buying x prints is given by the following.
b=−30.50-0.20x
What is the remaining balance on the card if Jenny bought 30 prints?
Answers
The remaining balance on the card is $24.50.
The balance on the card after buying the prints is the value of the gift card less the total cost of the prints
Balance = value of the gift card - total cost of the prints
Total cost of the prints = cost per print x number of prints bought
0.20 x 30 = $6
Balance = $30.50 - $6 = $24.50
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Lucy bought a desk on sale for $883. This price was 15% less than the original price.
Answers
the answer to the question is 898$
solve for value of x in simplest radical form
Answers
Answer:
3
Step-by-step explanation:
Find the value of x that makes △DEF∼△XYZ.
Answers
Answer:
x = 5
Step-by-step explanation:
5×2 = 10
8×2 = 16
so
2(3x-5) = 20
3x-5 = 10
3x = 15
x = 5
You are going on a camping trip with your family for 3 days. You decided that you need 5 batteries for your flashlights. At the very last minute you decide to extend the trip to 9 days.
a. Set up a proportion to solve for the amount of batteries you will need for the extended trip.
b. Solve the proportion for part a
Answers
Answer:
15 batteries
Step-by-step explanation:
a. We have
5 batteries = 3 days
5 batteries/3 days = 1
5 batteries/3 days
we need to convert this to 9 days, so
x amount of batteries = 9 days
x batteries / 9 days = 1
5 batteries / 3 days = x batteries / 9 days
b.
5 batteries / 3 days = x batteries / 9 days
multiply both sides by 9 days to get rid of the denominators as well as the days variable
5 batteries * 9 days / 3 days = x batteries
5 batteries * 3 = x batteries
15 batteries = x batteries
x = 15
The proportion for the given situation is 3 : 5 :: 9 : x and 15 batteries required for 9 days trip.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let x be number of batteries required for 9 days trip.
a) So, the proportion is
3 : 5 :: 9 : x
b) Solve for x, that is
3x=45
⇒ x=15
Therefore, the number of batteries required for 9 days trip is 15.
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can someone please help me i need to show the working out too
Answers
Answer:
(1) x=15/2
(2) x=1
Step-by-step explanation:
(1) 4x−1 /2 =x+7
2x+ −1 /2 =x+7(Distribute)
2x+ −1 /2 =x+7
Step 2: Subtract x from both sides.
2x+ −1 /2 −x=x+7−x
x+ −1 /2 =7
Step 3: Add 1/2 to both sides.
x+ −1 /2 + 1 /2 =7+ 1 /2
x= 15 /2
(2) 3x+2=( 2x+13)/ 3
3x+2= 2 /3 x+ 13 /3 (Distribute)
3x+2= 2 /3 x+ 13 /3
Step 2: Subtract 2/3x from both sides.
3x+2− 2 /3 x= 2 /3 x+ 13 /3 − 2 /3 x
7 /3 x+2= 13 /3
Step 3: Subtract 2 from both sides.
7 /3 x+2−2= 13 /3 −2
7 /3 x= 7 /3
Step 4: Multiply both sides by 3/7.
( 3 /7 )*( 7 /3 x)=( 3 /7 )*( 7 /3 )
X=1
Darren got 39 out of the 52 questions correct on a test. What percent of the questions did he get correct?
Answers
Answer:
75%
Step-by-step explanation:
Here are step-by-step instructions showing you how we calculated 39 out of 52 as a percentage:
The first step is to divide 39 by 52 to get the answer in decimal form:
39 / 52 = 0.7500
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.7500 * 100 = 75.00%
∣ x + 1 − x 2 ∣ = 2 ( 2 x 2 − 1 )=
Answers
Answer:
X = 7
Step-by-step explanation:
∣ x + 1 − x 2 ∣ = 6
∣ -x + 1 ∣ = 6
-7 + 1 = -6
Absolute value of -6 is 6
x = 7
The value of x for the expression is equal to 7.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The value of x is solved as,
∣ x + 1 − x 2 ∣ = 6
∣ -x + 1 ∣ = 6
-7 + 1 = -6
The absolute value of -6 is 6
x = 7
Therefore, the value of x for the expression is equal to 7.
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2. The area of a rectangle is 721 quare yards, M the length of the rectarije v fards, Wuch enpresion represent
the width of the rectangle in yards?
Answers
Answer:
721/M
Step-by-step explanation:
Length times width equals area so area (721) divided by length/width (M) = the corresponding length/width. (width)
how to simplify -5 1/4 - (-7 1/2
Answers
(hopefully I read this right)
-5 1/4 - (-7 1/2)
-5 1/4 - -7 1/2
-5 1/4 - -7 2/4
-21/4 - -30/4
-21/4 - -30/4 = 9/4 = 2 1/4
Hopefully I am correct!
I FORGOT TO PUT THE ANSWERS SORRY PLEASE HELP
Answers
Answer:
Step-by-step explanation:
Circumscribed means written around the outside. -scribe means writing and
think of how circumference is the distance around the outside of a circle. It is a little more special and specific...all the segments that make the triangle are tangents to the circle, that is, they only touch the circle at one point.
So the circle is inscribed-- that is, written inside of the triangle (in the same, special specific way).
Circle A is inscribed in triangle RST.
Answer:
Inscribed
Step-by-step explanation:
What is polygon inscribe?
When a polygon is inscribed inside another polygon it is called polygon inscribe.Here Circle A is drawn inside ∆RST so it's inscribed.I need help with this Graph!
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary). (-6,3) and (3, -9)
find leg number 1 and leg number 2 and the distance
Answers
Answer:
Step-by-step explanation:
The distance between two points (-6, 3) and (3, -9) is 10.81 units.
We have a graph a right triangle with the two points A(-6,3) and B(3, -9) forming the hypotenuse.
We have find the distance between the two points using only the sides of the right triangle.
What is the formula to find the distance between the two points on Cartesian plane ?The distance between two points -
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
According to the question, we have -
Coordinates of Point A = (- 6, 3)
Coordinates of Point C = (3, -9)
Now -
Coordinates of Point B will be (- 6, -9) [formed by the intersection of sides].
Distance AB -[tex]AB = \sqrt {\left( {-6 - (-6) } \right)^2 + \left( {3 - (-9 } \right)^2 }[/tex] = 6 units
Distance BC -[tex]BC = \sqrt {\left( {-6 - 3 } \right)^2 + \left( {-9 - (-9 } \right)^2 }[/tex] = 9 units
Using the Pythagoras theorem -
[tex](AC)^{2} =(AB)^{2} +(BC)^{2}[/tex]
[tex](AC)^{2} =[/tex] 36 + 81
AC = [tex]\sqrt{117}[/tex] = 10.81
Hence, the distance between two points (-6, 3) and (3, -9) is 10.81 units.
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