The required function will be
y= 500-10x
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
let amount of money = x and
number of remaining candy =y
total 500 remaining candies= total 10x amount of money
y= 500-10x
To learn more about function
visit-: https://brainly.com/question/12431044
#SPJ9
6. The Golden Gate Bridge was built at a height of 300 m over San Francisco
Bay. From the ends of the bridge, the angles of depression to a tugboat in
the middle of the river are 25° and 32° respectively.
Find the length of the bridge.
The length of the golden gate bridge is -163.250975.
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
What is length?
Length is a measure of distance. According to the International System of Quantities, length has the dimension of distance. Most measurement systems select a length base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.
Given that,
The height of the bridge is 300m,
The angle of depression in the middle of the river are 25⁰ and 32⁰ respectively.
[tex]\frac{300}{tan(32)}[/tex] -[tex]\frac{300}{tan(25)}[/tex],
[tex]\frac{300}{0.624869}[/tex]-[tex]\frac{300}{0.466308}[/tex],
= -163.250975.
The length of the golden gate bridge is -163.250975.
To know more about trigonometry, visit:
https://brainly.com/question/22986150
#SPJ9
what relationship must hold for the point to be equidistant from the origin and the xz-plane? make sure that the relationship you state is valid for positive and negative values of a, b, and c
The relationship must hold for the point to be equidistant from the origin and the x z-plane is a^2+b^2+c^2 > b^2.
What is equidistant point:
A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.
Now,
distance from P(a, b, c) and the Origin (0,0,0)
[tex]\sqrt{(a-0)^2+(b-0)^2+(c-0)^2} =\sqrt{a^2+b^2+c^2}[/tex]
distance from p(a ,b, c) and the x-z plane
[tex]\sqrt{(0-0)^2+(b-0)^2+(0-0)^2} = |b|[/tex]
Here,
P is equidistant from the Origin and the x - z plane
[tex]\sqrt{a^2+b^2+c^2} = |b|[/tex]
[tex]a^{2} +b^2+c^3 = b^2[/tex]
[tex]a^{2} +c^2 = 0[/tex]
Hence a=c=0 ,thus the point P must be of the form (0,b,0) for any b ∈R
Again,
point P far the from the origin than from the x z plane
[tex]\sqrt{a^2+b^2+c^2} > |b|[/tex]
[tex]a^{2} +b^2+c^2 > b^2[/tex]
[tex]a^{2} +c^2 > 0[/tex]
Hence a, c ∈R such that atleast one of the a ,b ,c is non-zero.
Therefore,
(a ,b ,c) for any b∈ R and for a, c ∈ R with atleast one of the a and c is non-zero.
To know more about "Equidistant"
Refer this link:
https://brainly.com/question/1286346
#SPJ4
Which length of time is between 11.20 am and 2.05 pm ?
Answer:
2 hours 45 minutes.
Step-by-step explanation:
12.00 - 11.20 = 40 minutes
2. 05 = 14.05
14.05 - 12.00 = 2.05 = 2 hours 5 minutes
Answer = 2 hours 45 minutes.
Which angle number represents the linear pair of \angle FHC∠FHC?
The angle number that represents the linear pair of angle FHC is: angle 5.
What is the Linear Pair?The linear pair consists of two adjacent angles that are on a straight line, whose sum will be equal to 180 degrees when added together.
Thus, the two adjacent angles share a common side and a common vertex, and they are supplements of each other. That is, they have a sum of 180 degrees.
Angle 4 represents angle FHC. Angle 5 is adjacent to angle 4, and both lie on a straight line.
Therefore, angle FHC + angle 5 = 180 degrees.
In conclusion, we can state that, the angle number that represents the linear pair of angle FHC is: angle 5.
Learn more about the linear pair on:
https://brainly.com/question/13218054
#SPJ1
What is each logarithm expanded?
a. log₃ 250/37
We need to know about logarithm to solve this problem. The logarithm expanded is [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
Logarithm is the power to which a base should be raised to get a given number. Expanding logarithm is writing logarithms usisng addition, subtraction, simplifying the logarithm. In logarithm, log ab can be written as log a+ log b and log a/b can be written as log a -log b, [tex]log_{a} b[/tex] can be written as log b/log a. We will be using these rules to expand the given logarithm. In the given logarithm we have the base of the log as 3 and we have logarithm of fraction, which we can expand.
[tex]log_{3} \frac{250}{37} =log_{3} 250 - log_{3} 37=\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
So we found the expansion of the given algorithm using the rules for expansion of algorithm to be [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex].
Learn more about logarithm here:
https://brainly.com/question/14393032
#SPJ9
The points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2. If HK=45, find HJ.
Will give brainliest
When the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2 ,the value of HJ is 27.
How to illustrate the information?Fronxrye information, the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2.
Therefore, the value of HJ will be:
= (1 + 2)/(1 + 2 + 3) × 45
= 3/5 × 45
= 27
Therefore, the value of HJ is 27.
Learn nore about ratio on:
brainly.com/question/2328454
#SPJ1
-can someone help me 4d+3 if d=-1
Answer:
7
Step-by-step explanation:
-4d+3
-4(-1) + 3 Insert -1 for d
4+3=7
Charlotte is visiting Brazil and is looking at souvenirs to purchase. She finds a jersey that costs 110 Brazilian real. If the current exchange rate is 1 dollar:5.43 Brazilian real, how much does the jersey cost in U.S. dollars?
a. $4.94
b. $20.26
c. $104.57
d. $597.30
PLS HELP WILL GIVE BRAINLIEST!!!!
Answer: 36 degrees
Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees
Answer:
A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45
Find the amount in a continuously compounded account for the given conditions.principal: $ 1000 annual interest rate: 4.8% time: 2 years
A = $ 1100.76 the amount in a continuously compounded account for the given conditions.
What does compound interest entail?
Compound interest is when you receive interest on both your interest income and your savings. Let's imagine you invest $1,000 (your principal) and it earns 5% once a year in interest or profits (the compounding frequency).principal: $ 1000 annual
interest rate: 4.8%
time: 2 years
We know that continuously compound interest
A = [tex]P_{0} e^{rt}[/tex]
= [tex]1000 e_{(0.048)(2)}[/tex]
= [tex]1000 (e)^{0.096}[/tex]
= [tex]1000 ( 1.10075906 )[/tex]
= 1100 . 75906
A = $ 1100.76
Learn more about Compound interest
brainly.com/question/14295570
#SPJ4
4xsquared-1 factories
Answer:
That is a quadratic equation and must be factorized using two brackets. It is just a little confusing to recognize it as a quadratic as the middle x value is not there so we treat it as 0 - which means the two numbers must cancel each other out:
(2x + 1) (2x - 1)
Step-by-step explanation:
help
Answer:
(2x - 1)(2x + 1)
Step-by-step explanation:
4x² - 1
is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
4x² - 1
= (2x)² - 1²
= (2x - 1)(2x + 1)
Solve. Check for extraneous solutions. √3-x+ √x+2=3 Solve.
estimate 180 x 586 rounding
Answer:
12,000
Step-by-step explanation:
Since we're just estimating, we can just round the two numbers.
180 rounded to the nearest hundred is 200.
586 rounded to the nearest hundred is 600.
200 * 600 = 12,000
Therefore, 180 * 586 is roughly 12,000.
Tell which set or sets the 8 belongs to: natural numbers, whole, numbers, integers, rational numbers, irrational numbers, or real
numbers.
The number 8 is a natural number, whole number, integer, rational number, real number.
All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well. In this post, let's study all there is to know about whole numbers.
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers.
Real number is a value of a continuous quantity that can represent a distance along a line. Real numbers can be defined as the union of both rational and irrational numbers.
To know more about real numbers visit:
https://brainly.com/question/551408
#SPJ9
a. What is the solution of √5 x-1 +3=x ? Check your results.
The solution is 10
Firstly rewriting the equation to frame the steps of solution -
√(5x-1) + 3 = x
Shifting 3 to the Right Hand Side of the equation -
√(5x-1) = x - 3
Now taking square of both sides of the equation
(√(5x-1))² = (x - 3)²
On solving the square we get the equation -
(5x - 1) = x² + 9 - 6x
Further solving the equation -
5x - 1 - 9 = x² - 6x
5x - 10 + 6x = x²
x² - 11x + 10 = 0
Solving the equation by factorizing -
x² - 1x - 10x + 10 = 0
x (x - 1) - 10(x - 1) = 0
(x - 1) (x - 10) = 0
x = 1, 10
Keeping the value of x in equation to find the solution and check the results-
x = 1
√(5×1-1) +3 = 1
√(5 - 1) + 3 = 1
√4 + 3 = 1
2 + 3 = 1
5 = 1
x = 10
√(5×10-1) +3 = 10
√(50 - 1) + 3 = 10
√49 + 3 = 10
7 + 3 = 10
10 = 10
Since, 10 = 10, the result is correct.
Hence, the solution is 10
Learn more about calculations on solution of expression-
https://brainly.com/question/26430239
#SPJ4
Please help please I'll give brainlyest
[tex]\bf \implies{The \: correct \: option \: is \: (c) \: 240}[/tex]
Step-by-step explanation:[tex] \large \frac{40}{5} . \: 6 \: . \: \frac{10}{2} [/tex]
Step 1) : Cross out the common factor
[tex] \bf \longrightarrow\frac{ \cancel{40}}{ \cancel{5}} . \: 6 \: . \: \frac{ \cancel{10}}{ \cancel{2} } \\ \\ \bf \longrightarrow8 \times 6 \times 5[/tex]
Step 2 : Multiply it
[tex] \bf \longrightarrow8 \times 6 \times 5 \\ \bf \longrightarrow8 \times 5 \times 6 \\\bf \longrightarrow 40 \times 6 \\ \bf \longrightarrow240[/tex]
Jackson has a points card for a movie theater. • He receives 35 rewards points just for signing up. • He earns 8.5 points for each visit to the movie theater. • He needs 154 points for a free movie ticket. Write and solve an equation which can be used to determine x, the number of visits Jackson must make to earn a free movie ticket.
The number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jackson has a points card for a movie theater. He receives 35 reward points just for signing up. He earns 8.5 points for each visit to the movie theater.
Let x be the number of visits Jackson must make to earn a free movie ticket.
8.5x + 35 = 154
8.5x = 154 - 35
8.5x = 119
x = 119/8.5
x = 14
Thus, the number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
When finding the intersection of two lines from both Algebra I and Geometry, you first "set the linear equations equal to each other. Find the intersection Doint of the two lines whose equations are shown below. Be sure to find both the x and y coordinates. y=5x+1 and y=2x -11
The intersection point of two lines are (-4 , -19)
The intersection point are those point where two line met of cut each other are called intersection point.
the given line of equation are
y = 5x + 1
y = 2x - 11
On solving these two equation we get the values as follow,
value of x = -4
value of y = -19
hence by this we can say the the intersection point of the above lines are
( -4 , -19 )
Read more of intersection point here:
https://brainly.com/question/14217061
#SPJ9
For questions 4-7, find the measures of the angles in the picture below.
(Questions shown in image)
Answer:
Measures of each angle are as follows:
4. ∠BXC = 20°
5. ∠FXE = 85°
6. ∠GXD = 75°
7. ∠BXF = 75°
Step-by-step explanation:
#4
∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°
#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°
#6
Angles ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°
Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°
#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°
If a rectangle has sides
5x + 7 and 2x + 2. What is the perimeter of the rectangle in terms of x in simplest
form?
Answer:
14x+18
Step-by-step explanation:
2(5x+7) + 2(2x+2)
10x+14+4x+4
14x+18
ng
Assessment
Math
S=
Analytics
e County Public Schools Foundational Skills in Mathematics, Grade 9 Checkpoint: Solve linear equations and inequalities 2
I-hr
Р
Recommendations
Some salespeople earn a commission that pays them a percentage of the price of the items
they sell. The equation I = hr + ps gives the income of a salesperson who receives an hourly
wage plus commission, where h is the number of hours worked, r is the hourly rate of pay, p
is the percent commission, and s is the dollar amount of the salesperson's sales.
Solve for s in terms of I, h, r, and p.
Submit
Skill plans
You have prizes to reveal!
Quest
answ
12
Tim
elap:
01
03
HR MI
Smarts
out of 1
in
Answer:
hope it helped!
Step-by-step explanation:
With the SmartScore, the learning process is rewarded and your students are constantly reassessed. When a student starts practicing a skill, the SmartScore ...
Missing: s h, r, p. Quest 12th Leap: MI
A quadratic function is shown on the graph.
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
The range of the quadratic function is {y |0 ≤ y < 9}
What is the range of a function?The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?From the question, we have the following parameters:
The parabola opens upwardVertex = (0, 0)Closed circle point = (-2, 4)Open circle point = (3, 9)Write out the vertex
So, we have
Vertex = (0, 0)
Remove the x value
y = 0
From the question, we have
The parabola opens upward
This means that the vertex is a minimum
So, the range is
y ≥ 0
Rewrite as
0 ≤ y
Recall that:
Closed circle point = (-2, 4)
Open circle point = (3, 9)
Remove the x values
Closed circle point = 4
Open circle point = 9
Remove the smaller y value
Open circle point = 9
This means that the highest value of y is at open circle point = 9
This is represented as
y < 9
So, we have
0 ≤ y and y < 9
Combine both
0 ≤ y < 9
Rewrite properly as
{y |0 ≤ y < 9}
Hence, the range of the quadratic function is {y |0 ≤ y < 9}
Read more about range at
brainly.com/question/2264373
#SPJ1
{y |0 ≤ y < 9}
The person above need the shine, im just making it simple
guys please help plsssssssss
Answer:
b = 15
Step-by-step explanation:
[tex]\frac{5\left(\frac{b-1}{2}-1\right)+2b}{3}\\5\left(\frac{b-1}{2}-1\right)+2b\\5\left(\frac{b-1}{2}-1\right)\\5\cdot \frac{b-1}{2}-5\cdot \:1\\5\cdot \frac{b-1}{2}\\\frac{\left(b-1\right)\cdot \:5}{2}\\\frac{5b-5}{2}\\\frac{5b-5}{2}-5\\\frac{5b-5}{2}-5+2b\\=\frac{5b-5}{2}+\frac{2b\cdot \:2}{2}\\=\frac{5b-5+2b\cdot \:2}{2}\\5b-5+4b\\5b+4b-5\\9b-5\\\frac{9b-5}{2}\\=\frac{9b-5}{2}-5\\=\frac{\frac{9b-5}{2}-5}{3}\\\frac{9b-5}{2}-5\\\frac{9b-5}{2}-\frac{5\cdot \:2}{2}\\[/tex]
[tex]=\frac{9b-5-5\cdot \:2}{2}\\9b-5-5\cdot \:2\\9b-5-10\\9b-15\\=\frac{9b-15}{2}\\=\frac{\frac{9b-15}{2}}{3}\\=\frac{9b-15}{2\cdot \:3}\\=\frac{9b-15}{6}\\\frac{3\left(3b-5\right)}{6}\\\frac{3b-5}{2}\\=\frac{3b}{2}-\frac{5}{2}\\\frac{3b}{2}-\frac{5}{2}=5+b\\=\frac{3b}{2}\cdot \:2-\frac{5}{2}\cdot \:2=5\cdot \:2+b\cdot \:2\\\frac{3b}{2}\cdot \:2\\\frac{3b\cdot \:2}{2}\\=3b\\-\frac{5}{2}\cdot \:2\\=\frac{5}{2}\cdot \frac{2}{1}\\=-\frac{5}{1}\\=-5\\5\cdot \:2\\=10\\=3b-5=10+b\cdot \:2[/tex]
[tex]\mathrm{Add\:5--both\:\:sides\:of\:the\:expression}\\3b-5+5=10+b\cdot \:2+5\\3b=2b+15\\\mathrm{Subtract}\\3b-2b=2b+15-2b\\\mathrm{Thus,}\\b=15[/tex]
Hope it helps. :-)
answer this and u will get 20 points
The rate of increase in the water pressure will be
0.000993 atmosphere per kilometers.
How to illustrate the information?From the information given,it should be noted that the water pressure on Mustafa was illustrated by 0.993 atmosphere per meter.
Therefore, it should be noted that the rate of increase per kilometers will be illustrated as:
1000 meters = 1 kilometer
This will be
= 0.993 / 1000
= 0.000993
This will be illustrated as 0.000993 atmosphere per kilometers.
Learn more about rate on:
brainly.com/question/25537936
#SPJ1
Solve. (x+1)³/₂-2=25
The values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
[tex] {(x + 1) }^{3/2} [/tex] - 2 = 25
Adding 2 on both the sides of the equation we get
[tex] {(x + 1) }^{3/2} [/tex] - 2 + 2 = 25 + 2
[tex] {(x + 1) }^{3/2} [/tex] = 27
On squaring both the sides of the equation we get
[tex] {x + 1}^{3/2 \times 2} [/tex] = 27²
(x + 1)³ = 729
Now, using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we get
x³ + 1 + 3x² + 3x = 729
x³ + 3x² + 3x - 728 = 0 : Equation 1
By hit and trial method x = 8 is the solution of the equation 1.
Now, by remainder theorem we can write the equation 1 as
x³ + 3x² + 3x - 728 = (x - 8)(x² + 11x + 91) + 0
On solving quadratic equation x² + 11x + 91, we get
x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a
x = -11+✓(11² - 4×1×91)/2×1 and -11-✓(11² - 4×1×91)/2×1
x = -11+✓(121 - 364)/2 and -11-✓(121 - 364)/2
x = -11+✓(-243)/2 and -11-✓(-243)/2
x = -11/2 + ✓243i/2, -11/2 - ✓243i/2
Thus, the values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
Know more about factors of equation -
brainly.com/question/12269038
#SPJ4
92x 4.6 divided by 2.3
Answer:
184
Step-by-step explanation:
92 x 4.6 is 423.2 then you divide it by 2.3 which gets you 184.
Answer:
184
92 times 4.6 = 423.2
423.2 divided by 2.3 = 184
Step-by-step explanation:
Hope it helps! =D
Solve each equation. Check for extraneous solutions. 5(3 x+1)¹/₄=10
The extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.
We are given an equation:
5(3 x + 1)^ ( 1 / 4) = 10
Divide each side by 5, we get that:
⁴√3 x + 1 = 2
Raise both sides to the power 4, we get that:
3 x + 1 = 2⁴
3 x + 1 = 16
3 x = 16 - 1
3 x = 15
x = 15 / 3
x = 5
Therefore, we get that, the extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ4
A school trip uses a 42-seater coach (excluding the driver’s seat).
36 students, 3 teachers and 3 parents go on the coach.
Each student pays £4.25 towards the cost of the coach. Each parent pays twice as much
as a student pays. The teachers travel for free.
The coach company charges £195 for the trip.
a Show that the money paid by the students and parents is not enough to pay for the
coach.
b How much should each teacher pay so that the cost of the coach is covered exactly?
c On the day of the trip, 8 students are ill and they get their money back. The
passengers on the coach share the extra cost equally. What is the extra payment for
each passenger?
Step-by-step explanation:
the total charge is £195.
we have 36 students. each paying £4.25.
we have 3 parents. each paying 2×£4.25 = £8.50
we have 3 teachers. each paying £0.
a.
the payments are
36×4.25 + 3×8.50 = 153 + 25.5 = £178.50
that is clearly below the total charge of £195.
there is a deficit of 195 - 178.5 = £16.50
b.
3 teachers.
so, each should pay
16.5 / 3 = £5.50
c.
8 students drop out.
that means
8× 4.25 = £34.00 are not paid.
we have now
28 students
3 parents
3 teachers
on the bus.
these are 34 persons.
34 / 34 = £1.00
they each would have to pay £1.00 as extra payment.
put these numbers in least to greatest form7.25, -9.8, 0
Answer:
7.25, 0, -9.8
Step-by-step explanation:
Raj wrote -(5^4) = (-5^4). Is Raj correct? Why or why not?
Raj is incorrect as the negative signs are put in different place.
What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
given:
-(5^4) = (-5^4).
Raj is incorrect because the in LHS part the negative sign is out of the exponent term and in RHS part the negative sign is within exponent.
-(5^4) gives - 625
and, (-5^4) gives 625
Learn more about integers here:
https://brainly.com/question/18411340
#SPJ1