The cost of 8 rides will be equal to $65 and the equation for the r rides will be equal to $25 + $5(r).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Price of admission into the park = $25
Price to pay for every ride in the park = $5
(a)
Then, the price to pay for 8 rides will be,
$25 + $5(8)
= $25 + $(40)
= $65
(b)
Then, the equation for the price to pay for r rides will be equal to,
$25 + $5(r)
Here, r is the number of rides.
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[tex]\huge\fbox\purple{Question}[/tex]
1)find L.C.M of the following set of numbers by listing multiplies
a)6 and 9
b)8 and 12
c)4,6 and 8
2)find L.C.M of the following set numbers by using divison method
a)6 and 15
b)20 and 30
c)25,30 and 75
The LCM of the given numbers have been determined.
What is LCM ?LCM stands for Least Common Multiple .
For two numbers , LCM is the number that is the smallest number of which they both are a factor.
It is asked to determine
LCM of 6 and 9
6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}
9 = { 9 , 18 ,27 .....}
The LCM of 6 , 9 is 18
LCM of 8 and 12
8 = { 8,16,24,32....}
12 = {12 , 24 ,36....}
The LCM of 8 and 12 is 24
LCM of 4 , 6 and 8
4 = {4 , 8 , 12 , 16 , 20,24,28 ....}
6 = { 6 ,12 ,18,24......}
8 = {8 , 16,24 .....}
The LCM of 4,6 and 8 is 24
The LCM of 6 and 15 is 30
The LCM of 20 and 30 is 60
The LCM of 25,30 and 75 is 150
The image of the solution is attached .
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The inverse of the function f(x) = 1/2x + 10is shown.
h(x) = 2x-0
What is the missing value?
Answer:
20
Step-by-step explanation:
the inverse of
y=1/2x + 10
is
x=1/2y+10
from here you just solve for y
x-10 = 1/2y
2(x-10) = y
2x-20 = y
Wendy and two friends went out to eat and decided they would split the bill. The total bill was 35.40. They also decided to leave a 20% tip. What is the price that each person paid?
Answer:
14.16
Step-by-step explanation:
we first calculate the total amount of money paid, which is 35.40 plus 20%, we use this calculation:
35.40×1.20 = 42.48
now, this amount is split to 3 people, so:
42.48/3 = 14.16
and that is our answer
Find the common multiple of 5 and 6 between 100 mathfind the common multiple of 5 and 6 between hundred
Answer
100 multiples of 5 greater than 100 are:
Step-by-step explanation:
105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 380, 385, 390, 395, 400, 405, 410, 415, 420, 425, 430, 435, 440, 445, 450, 455, 460, 465, 470, 475, 480, 485, 490, 495, 500, 505, 510, 515, 520, 525, 530, 535, 540, 545, 550, 555, 560, 565, 570, 575, 580,
n + 7
------- = 2
13
Answer:
19
Step-by-step explanation:
(n+7)/13 = 2 [given]n+7=26 [multiply both sides by 13]n=19 [subtract 7 from both sides]i need the missing blank....
Simplify the expression below. How many digits are in the answer?
2.784 - 3.00079 + 10.671 x 1.0798
Answer:
11.3057558
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct statements are options C and option D.
- 6x + 15 < 10 - 5x ⇒ 3rd answerAn open circle is at 5 and a bold line starts at 5 and is pointing to the right.What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
The inequality is -3(2x - 5) < 5(2 - x)
At first, simplify each side
-3(2x - 5) = -3(2x) + -3(-5)
Remember (-)(-) = (+)
-3(2x - 5) = - 6x + 15
5(2 - x) = 5(2) + 5(-x)
Remember (+)(-) = (-)
5(2 - x) = 10 - 5x
- 6x + 15 < 10 - 5x
Subtract 15 from both sides
- 6x < -5 - 5x
Add 5x to both sides
- x < - 5
Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality
The coefficient of x is -1
Divide both sides by -1
x > 5
Therefore the correct statements are options C and option D.
- 6x + 15 < 10 - 5x ⇒ 3rd answerAn open circle is at 5 and a bold line starts at 5 and is pointing to the right.To know more about inequality follow
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Solve for x in the equation
X
O x=-11±25
O x=-11+25
0 x--11+5√/5
Ox--11,5/5
2
x²+11x+121-125
4
=
Answer:
The answer for this question is c
The value of x from the quadratic term equation is x = ( -11/2 ) ± ( 5√5 ) / 2
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 11x + 121/4 = 125/4
Subtracting ( 125/4 ) on both sides , we get
x² + 11x + ( 121 - 125 ) / 4 = 0
x² + 11x - 1 = 0 be equation (1)
On simplifying , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
So , x = [ -11 ± √ ( 11 )² - 4 ( 1 ) ( -1 ) ] / 2
On further simplification , we get
x = -11 ± √ ( 121 + 4 ) / 2
x = [ -11 ± √125 ] / 2
x = ( -11/2 ) ± ( 5√5 ) / 2
Therefore , the roots of the equation are x = ( -11/2 ) ± ( 5√5 ) / 2
Hence , the quadratic equations are solved
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which of the following functions best describes this graph?
A.y=(x-1)(x-1)
B.y=x^2-5x+6
C. y=x^2-x+5
D. y=( x-3)(x+1)
Answer: y = (x-1)(x-1)
Step-by-step explanation:
There is pretty much no vertical shift so that immediately rules out B and C.
We can solve y = (x-1)(x-1) and get x = 1
The graph shows x = 1 as a zero, so we know this graph is correct.
Quentin currently owes a total of $1,551.42 on his revolving credit accounts. What is Quentin's debt-to-credit ratio if his total revolving credit limit is $8,619.00? (4 points)
18%
23%
29%
31%
Answer:
(a) 18%
Step-by-step explanation:
The debt to credit ratio is found by dividing his debt by his credit limit.
__
using the definitionratio = debt/credit limit = $1551.42/$8619.00 ≈ 0.18 = 18%
Quentin's debt to credit ratio is 18%.
A dog sits at a corner of a square with side length 44 meters. the dog runs 10 meters along a diagonal toward the opposite corner. it stops, makes a 90 degrees right turn and runs 5 more meters. a scientist measures the shortest distance between the dog and each side of the square. what is the average of these four distances in meters?
Refer to the figure given below while reading the solution.
Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.
And then position B when traveled 5 m towards the right turning 90°.
We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).
Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).
Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.
The shortest distance of B from PQ = AC-ADThe shortest distance of B from SR = 44-(AC-AD)The shortest distance of B from SP = AC+ADThe shortest distance of B from RQ = 44-(AC+AD)So, the average of the shortest distances of B from each side is [tex]\frac{(AC-AD)+44-(AC-AD)+(AC+AD)+44-(AC+AD)}{4}=\frac{44+44}{4}=22[/tex]
Hence, the average of the shortest distance of B from each side is 22 m
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g(t)=2.0.4^t for t = -2
Answer:
2(0.4)^-2 = 12.5
Step-by-step explanation:
do math noob
In a factory, the chance that a certain machine works without overheating in the morning is 50%. if it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. what is the probability that on a given day it will work in the morning and overheat later on? a. 4% b. 3.75% c. 7.5% d. 3.5%
Answer: C. 7.5%
Solve as decimal
0.5*0.15=0.075
Move two decimal points over
0.075 -> 7.5
Change back to percent
7.5%
Mo travels 30 miles in 45
minutes.
He then travels 18 miles in 30
minutes.
Calculate his average speed.
Answer:
38.4 miles per hour
Step-by-step explanation:
30 miles in 45 minutes
18 miles in 30 minutes
Average speed = total distance / total time
= (30+18) / ( 45 min + 30 min)
= 48 miles / ( 1.25 hr ) = 38.4 miles per hour
What is the distance from -5 to 0?
0, because 151=0
O 5, because 1-51=5
O5, because 1-51=-5
O-5, because 1-51 = -5
7 of 23 QUESTIONS
SUBMIT
Answer:
distance between -5 to 0 = 5 units
25. Given: TE= RI, TI = RE,
Proof
LTDI and LROE are right /
Prove: TD=RO
Answer:
In triangle TEI and ERI
TI = RE ( given)
angle TDI = angle ROE ( given).
TE = RI ( given).
by side angle side criteria
both the triangles are congruent
by cpct ( corresponding parts of congruent triangles)
TD is congruent to RO
Calculate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\dfrac{\log(x^8 - 5)}{x^2}}[/tex]
If we evaluate at infinity, we have:
[tex]\bf{\displaystyle L = \lim_{x \to \infty}{\frac{\log(x^8 - 5)}{x^2}} = \frac{\infty}{\infty} }[/tex]
However, the infinity of the denominator has a higher order. Therefore, we can conclude that [tex]\boldsymbol{L = 0.}[/tex]
However, proving that the limit is 0 without using L'Hopital or the "order" criterion is complicated. To do so, let us denote:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} }[/tex]
To find the limit, we must look for two functions h(x) and g(x) such that h(x)≤ f(x)≤ g(x) and
[tex]\boldsymbol{\displaystyle \lim_{x \to \infty}{h(x)} = 0, \qquad \lim_{x \to \infty}{g(x)} = 0}[/tex]
If we find these functions, then we can conclude that [tex]\bf{\lim_{x \to \infty}{f(x)} = 0.}[/tex]
First, let's note that when x⁸ - 5 > 1, then log(x⁸ - 5) > 0 (and this is true when x is large). Likewise, we have that x² > 0 for x > 0. Therefore, we have:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} \geq 0}[/tex]
when x "is big enough". Thus, we have h(x) = 0 where it is clear that [tex]\bf{\lim_{x \to \infty}{h(x)} = 0.}[/tex]
To find the second function, let's first note that \log is an increasing function, so since x⁸ ≥ x⁸ - 5, then log(x⁸) ≥ log(x⁸ - 5). So we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} }[/tex]
now, if we take y = e^y, then we can write
[tex]\boldsymbol{\displaystyle \frac{\log(x^8)}{x^2} = \frac{\log(e^{8y})}{e^{2y}} = \frac{8y}{e^{2y}}}[/tex]
A very important property about the exponential function is
[tex]\boldsymbol{\displaystyle e^x > \frac{x^n}{n!}}[/tex]
For any n [tex]\bf{n \in \mathbb{N}}[/tex] and x > 0. If we take n = 2, then we have
[tex]\boldsymbol{\displaystyle e^{2y} > \frac{(2y)^2}{2!} = \frac{4y^2}{2} = 2y^2}[/tex]
From this it follows that
[tex]\boldsymbol{\displaystyle \frac{1}{e^{2y}} < \frac{1}{2y^2} }[/tex]
Therefore, we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} < \frac{8y}{2y^2} = \frac{4}{y} = \frac{4}{\log x} }[/tex]
yes, [tex]\bf{g(x) = 4/\log x}[/tex] where [tex]\bf{\lim_{x \to \infty}{g(x)} = 0}[/tex]. Also, [tex]\bf{h(x) \leq f(x) < g(x)}[/tex]. Therefore, [tex]\bf{\lim_{x \to \infty}{f(x)} = 0}[/tex].
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]
Im bad at composite figures || please hurry
The figure is the combination of trapezoid and square. Then the area of the figure will be 39 square meters.
The complete question is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is the combination of trapezoid and square.
Then the area of the geometry will be
Area = Area of trapezoid + Area of square
Area = 1/2 x (3 + 9) x 5 + 3 x 3
Area = 30 + 9
Area = 39 square meters
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Hi 6 questions ! They are practice so shouldn’t be to hard!
Please fine the slope through the given points
Answer:
1. 1
2. 6/5
5. 0
6. -1/2
9. -1
10. 0
Step-by-step explanation:
Well you should just the slope formula (y2-y1)/(x2-x1)
1. (8-5)/(0-(-3)) = 3/3 = 1
2. (-3-(-9))/(4-(-1)) = 6/5
5. (3 - 3) / (0-2.5) = 0/(-2.5) = 0
6. (0-(-4))/(0-8) = 4/(-8) = -1/2
9. (4-1)/(9-12) = 3/(-3) = -1
10. (7-7) / (1-(-5)) = 0/6 = 0
which statement is correct?
Answer:
the first one
Step-by-step explanation:
0.0206×0.188<0.0769/0.000023
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
Answer:
I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.
Step-by-step explanation:
See attached graph.
The value of f(–10) = 82 False
f(-10) = (-10)^2 - 5*(-10) + 12
f(-10) = (100) +50 + 12
f(-10) = 162
The graph of the function is a parabola. True
The graph of the function opens down. False
The graph contains the point (20, –8). False
The graph contains the point (0, 0). False
timmy makes a table to keep track of the number of visitors to his new websites as time progresses: is the data he collected best modeled by an exponential or linear function
Answer:
Show the process
There are boys and girls in a class in the ratio 1: 12 there are 77 more girls than boys. how many boys are there?
Let's set up some variables:
b: # of boysg: # of girlsLet's set up some equations based on the informative given:
boys to girls ratio ⇒ 1: 12(Mathematical form) g = 12b
77 more girls than boys(Mathematical form) g = b + 77
Let's put the equation together:
g = 12b -- equation 1
g = b + 77 -- equation 2
(equation 2)'s value of g into (equation 1)
12b = b + 77
11b = 77
b = 7
There are 7 boys.
Answer: 7 boys
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9. Solve for x: Please explain
Answer:
since the triangle has a line on 2 sides, it means that it is equal. Also, every triangle has 180 degrees so the missing degree is 70
Step-by-step explanation:
Figured it out
Answer:
x = 70°
Step-by-step explanation:
Since 2 sides are marked as congruent then the triangle is isosceles with 2 base angles being congruent , both 55°
the sum of the 3 angles in the triangle = 180° , so
x + 55° + 55° = 180°
x + 110° = 180° ( subtract 110° from both sides )
x = 70°
can someone help me with this problem pleaseee
Answer:
x-intercept: (-5, 0)
y-intercept: (0, -4)
Step-by-step explanation:
The x-intercept is as the name implies when the line intersects the x-axis (the horizontal axis) or when y is equal to 0. If you look at the graph it intersects the x-axis at (-5, 0). The y-intercept follows the same concept except it's when it intersects the y-intercept (vertical axis) or when x is equal to 0. If you look at the graph it, it intersects the y-axis at (-4, 0).
does someone mind helping me with this problem? Thank you!
The circumcenter is the center of the. circle
The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.
The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.
Answer: Another name of circumcenter is, " Circumscribed circle ". The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of the polygon's vertices & the center of that circle is called the circumcenter. All polygons that have circumcircles are known as cyclic polygons. However, all polygons does not have a circumcircle. Only regular polygons, triangles, rectangles, and right-kites can have the circumcircle and thus the circumcenter as well.
You may find that the circumcenter of a triangle as the most common thing asked in exams and it is generally what schools begin with. So, some brief information about the circumcenter of a triangle is given below. You may safely ignore them if you haven't learned them yet.
The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (meeting at one point). All triangles are cyclic and hence, can circumscribe a circle, therefore, every triangle has a circumcenter.
Property 1: All the vertices of the triangle are equidistant from the circumcenter.
Property 2: All the new triangles formed by joining O to the vertices are Isosceles triangles.
Property 3: Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle
Property 4: In an acute-angled triangle, circumcenter lies inside the triangle
Property 5: In an obtuse-angled triangle, it lies outside of the triangle
Note- Location for the circumcenter is different for different types of triangles.
The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:
Step 1: Draw the perpendicular bisector of any two sides of the given triangle.Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be noted that, even the bisector of the third side will also intersect at P.P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]
∩_∩
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┏━∪∪━━━━┓
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Find the volume of a cube with side lengths of 12 cm
Answer:
1728 cm³
Step-by-step explanation:
Finding the volume of a cube is a simple process that is easy to remember. The formula for finding the volume of a cube is commonly taught as L × W × H (Length × Width × Height). This formula also works with finding the volume of rectangular prisms.
Since the shape you're finding the volume of is cube, the length is equal to its width as well as its height.
The first step of this problem is to plug in known values to the formula. Since length L = 12 cm, width W and height H are also equal to 12 cm.
12 × 12 × 12 is the new expression. The next step is to simplify this expression by multiplying.
Based on times tables, 12 × 12 = 144. So, the expression can be partially simplified to 144 × 12 for easier multiplication.
144 × 12 can be split into an addition problem based on the Distributive Property of Multiplication:
144 × (10 + 2) Expand the expression to remove parentheses.
144 × 10 + 144 × 2 Multiply 144 × 10 and 144 × 2.
1440 + 288 Add the two addends.
1728 Remember to add back the units!
1728 cm³
The volume of a cube with side lengths of 12cm is 1728 cm³.
Note:
This step-by-step explanation is for better understanding how to do this mentally or without a calculator. In a calculator, finding the volume of a cube can be found by inputting either of these:
(Side Length) × (Side Length) × (Side Length) =
(Side Length) [(x³) or (³), depending on the model of calculator] =
if sin theta=-3/5 in quadrant III what is cos theta
Answer:
Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 4.
Step-by-step explanation:
