After we evaluate the function f at the indicated values the results are
a. (4) −11, (5) −52, (6) 0
b. (4) -1, (5) −17, (6) -5
c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a
d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a
What is function?A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.
Lets evaluate the function a. f(-3)
4. f(-3) = 2(-3)-5
= −11
5. f(-3) = −5(-3)²+2(-3)−1
= −52
6. f(-3) = -3-1-(-3)+1
= 0
Lets evaluate the function b. f(2)
4. f(2) = 2(2)-5
= −1
5. f(2) = −5(2)²+2(2)−1
= −17
6. f(2) = -3-1-(2)+1
= −5
Lets evaluate the function c. f(-a)
4. f(-a) = 2(-a)-5
= −2a−5
5. f(-a) = −5(-a)²+2(-a)−1
= −5a² −2a−1
6. f(-a) = -3-1-(-a)+1
= −3+a
Lets evaluate the function d. -f(a)
4. -f(a) = -(2(a)-5)
= −2a+5
5. -f(a) = -(−5(a)²+2(a)−1)
= 5a² −2a+1
6. -f(a) = -(-3-1-(a)+1)
= 3+a
Learn more about functions
https://brainly.com/question/11624077
#SPJ13
4x + 7 = 23 S = {3, 4, 5, 6}
Answer:
4
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*x+7-(23)=0
Pull out like factors :
A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
4x - 16 = 4 • (x - 4) = 0
x-4 = 0
Add 4 to both sides of the equation :
therefore, x = 4
To know more about linear equations, visit: https://brainly.in/question/48653350?referrer=searchResults
#SPJ1
What number belongs in the blank space in the recursive formula?
The recursive formula of the arithmetic sequence is
[tex]a_n=a_{n-1}+d[/tex]Where d is the common difference between each 2 consecutive terms
The explicit form of the arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
Since the given explicit form of the sequence is
[tex]a_n=13+(n-1)6[/tex]Then
a = 13
d = 6
The recursive form of the sequence should be
[tex]a_n=a_{n-1}+6[/tex]The missing number is 6
The answer is D
X2-6x+4=0 slice by completing the square
Answer:
See below
Step-by-step explanation:
x^2 -6x = - 4
take 1/2 of the x coefficient, square it , and add to both sides
x^2 - 6x + 9 = -4 + 9
(x-3)^2 = 5 now sqrt both sides
x-3 = +- √5
x = 3 ± √5
Answer:
xπg73 xueu iwkwbsjdhhsd
The connective "⇒ " in logic is a…
The binary connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B). It can be read « A implies B », « A is a sufficient condition for B », or « B is a necessary condition for A ».
What is connective?
Connective is function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and returns a single truth value as output.
What is logical connective?
A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.
Generally there are five connectives which are −
OR (∨)
AND (∧)
Negation/ NOT (¬)
Implication / if-then (→)
If and only if (⇔).
connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B).
To know more about logical connective, visit:
https://brainly.com/question/28258509
#SPJ9
15. TRAVEL The formula s = √18d can be used to find the speed s of a
car in miles per hour when the car needs d feet
to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after
slamming on the brakes, estimate the speed of the car.
The speed of the car associated with a braking distance of 12 feet is approximately equal to 14.697 miles per hour.
What is speed associated with a given braking distance?
In this problem we find a radical equation that describes the speed (s), in miles per hour, and the braking distance (d), in miles. If we know that d = 12 ft, then the initial speed of the car is:
s = √(18 · d)
s = √[18 · (12)]
s = 6√6 ft
s ≈ 14.697 mi / h
The initial speed of the car is approximately 14.697 miles per hour.
To learn more on radical functions: https://brainly.com/question/27847549
#SPJ1
You are solving a measurement problem where the numbers 5.2187 x 10−3, 2.05 x 107, and 3.40 x 103 are multiplied. How many significant digits should the product have?
5
3
2
1
The number of significant digits that the product have is 3.
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures.
Rules for determining Significant Numbers,
Within the specified measurement or reporting resolution, non-zero digits are significant.Significant zeros occur between two significant non-zero digits (significant trapped zeros).Leading zeros (zeroes to the left of the first non-zero digit) is not important.The trailing zeros (zeroes after the final non-zero digit) in a decimal number are important if they fall within the measurement or reporting resolution.The trailing zeros (zeroes after the final non-zero digit) in a decimal number are important if they fall within the measurement or reporting resolution.Given Numbers are [tex]5.2187 * 10^{-3}, 2.05 *10^{7} and 3.40 * 10^{3}[/tex]
Now, Multiplying the given numbers,
[tex]5.2187 * 10^{-3}* 2.05 *10^{7} * 3.40 * 10^{3} =3.64 *10^{8}[/tex]
So, In 3.64 *10^8, The number of significant digits is 3.
To read more about significant numbers visit https://brainly.com/question/14804345
#SPJ1
Answer:
answer is 3
Step-by-step explanation:
Maria has $40, which is 170% of the amount that Kelly has. How much money, in dollars, does Kelly have?
We need to know about percentage to solve the given problem. The amount of money that Kelly has in dollars is approximately $24.
Percentage is a number or ratio expressed as a ratio or fraction of 100. If for example we have to find out one-fourth of a quantity then we can say that we need to find 25% of the quantity. In the given question we know that Maria has $40 which is 170% of the money that Kelly has, we need to find out the amount of money that Kelly has.
170/100x a=40
a=40x100/170=23.5
Therefore the amount that Kelly has in dollars is $23.5 approximately $24.
Learn more about percentage here:
https://brainly.com/question/1053881
#SPJ1
Which is an equation of a direct proportion? y=8x y=
12x+4 y=12x y=4x−4
The equation of a direct proportion is A. y=8x.
What is a direct proportion?It should be noted that a direct proportion is also a direct variation. It is one when the relation between the two quantities have a value that's constant.
In this case, it's illustrated as y = 8x.
Let's say x = 1 y will be = (8 × 1) = 8
When x = 2, y = (8 × 2) = 16
In this case, it should be noted that the constant of 8 is illustrated.
In conclusion, the correct option is A.
Learn more about proportion on:
brainly.com/question/13742765
#SPJ1
What if Tanisha needs 40 bowls for the picnic? Explain how to write an equation with a letter for an unknown factor to find the num er of packs she should buy. Than find the unknown factor.
We know that each pack has 6 bowls and we need 40 bowls. Let x be the number of packs, then we can write:
[tex]6x=40[/tex]If we move the coefficient of x to the right hand side, we get
[tex]x=\frac{40}{6}[/tex]which gives x= 6.666.
However, the number of packs are integer numbers, so we must round up to the nearest integer. Hence, the answer is 7 packs.
Sarah used 3.5 cups of cheese in a dish that serves 10 people. What constant of proportionality relates the number of servings to cups of cheese?
0.35
0.05
0.5
0.25
In a case whereby Sarah used 3.5 cups of cheese in a dish that serves 10 people the constant of proportionality that relates the number of servings to cups of cheese is 0.35.
How can the proportionality constant be determined?We were told that Sarah used 3.5 cups of cheese with 10 people, this can be written as :
let the c= the cups of cheese which is 3.5 cups of cheese
let n = number of the people that is been served
Then the equation can be written as :
c∝n
then we can bring in the proportionality constant sign as ;
then c=kn
then we can introduce the given figures into the equation as ;
3.5=k *10
the we can determine the value of the constant as :
k=3.5/10 = 0.35
Therefore, option A is correct.
Learn more about proportionality at:
brainly.com/question/28413384
#SPJ1
ABCand XYZ are similar triangles. The lengths of the two sides are shown. Find the lengths of the third side of each triangle
Given:
AC = 9.6
AB = 4
BC = a
XZ = y
XY = 2.5
YZ = 7.5
To find the lengths of the third side of each triangle apply the ratio for similar triangles.
Since both triangles are similar, the corresponding sides are proportional.
[tex]\frac{AC}{XZ}=\frac{AB}{XY}=\frac{BC}{YZ}[/tex]• For BC:
We have:
[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]Input values into the equation:
[tex]\begin{gathered} \frac{4}{2.5}=\frac{a}{7.5} \\ \\ \text{Cross multiply:} \\ 2.5(a)=7.5(4) \\ \\ 2.5a=30 \\ \\ \text{Divide both sides by 2.5:} \\ \frac{2.5a}{2.5}=\frac{30}{2.5} \\ \\ a=12 \end{gathered}[/tex]Therefore, the length of BC is 12.
• For XZ:
We have the equation:
[tex]\frac{AC}{XZ}=\frac{AB}{XY}[/tex]Input values into the equation:
[tex]\begin{gathered} \frac{9.6}{y}=\frac{4}{2.5} \\ \\ \text{Cross multiply:} \\ 4y=9.6(2.5) \\ \\ 4y=24 \\ \\ \text{Divide both sides by 4:} \\ \frac{4y}{4}=\frac{24}{4} \\ \\ y=6 \end{gathered}[/tex]Therefore, the length of XZ is 6
ANSWER:
• a = 12
• y = 6
Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 59 and in a separate drawing you must also select the correct single number between 1 and 30 find the probability of winning the jackpot
Winning the jackpot in a certain lottery requires you to pick two correct numbers between 1 and 59, and in a separate drawing, you also have a 7.32397915e-8 chance of winning when you also pick one correct number between 1 and 30.
A number of ways to select r items from n, nCr = n!/(r! x (n - r)!)
Number of possible methods to choose 4 winning numbers from 59 = 59C4
= 59!/(55! x 4!)
= 455,126
The number of possible ways to choose a single accurate number from 30 = 30.
The odds of winning the jackpot are 1/(probability) (Number of ways in which 4 winning numbers can be selected from 59 x Number of ways in which the correct single number can be selected from 30)
= 1/(455,126 x 30)
= 1/13653780
= [tex]7.32397915^{8}[/tex]
To learn more about probability
https://brainly.com/question/11234923
#SPJ1
Double quantity more than 5
Answer:
Any answer greater than 10 seems to work.
Step-by-step explanation:
This question is not that specific, but 5*2 is 10, so anything more than 10 would be more than double the quantity.
The graph of y = f(x) is shown below. 10 8 6 4B A 2 D 10 10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 ez 2 4 3 6 9 10 -6 -8 10 Which point could be used to find f(3)? A A B B D 1572 1001
The function is represented by the function
[tex]y=f(x)[/tex]To find f(3), we will find the point on the graph where we are given the value of x = 3:
[tex]\begin{gathered} f(3)\Rightarrow x=3 \\ y=f(3)=0 \\ f(3)=0 \end{gathered}[/tex]Therefore, the point that could be used to find f(3) is given by option A (A)
solve the following equation for x: 2x-3y=6
2x-3y=6
You have to pass the y term to the other side of the equation
2x=6+3y
Then divide by 2 to get the expression for x
[tex]x=\frac{6+3y}{2}[/tex]Consider the system of equations.
7j-h=9
3j+h=21
What is the value of j?
After considering the system of equations the value of j is 3.
What is a system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Types of systems of linear equations
Dependent: There are innumerable solutions for the system. The same lines are shown on the equation graphs.
Independent: There is just one solution for the system. The equations' graphs come together at a single point.
Inconsistent: There is no solution for the system. The equations' graphs are parallel lines.
Here. we have
The given system of equations is:
7j-h=9
3j+h=21
we simplify the given system of equations and get
h = 7j - 9
now, put the value of h in 3j+h=21 and get
3j + (7j-9) = 21
10j = 30
j = 3
h = 12
Hence, after considering the system of equations the value of j is 3.
To learn more about the system of equations from the given link
https://brainly.com/question/12526075
#SPJ1
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
option 1 (amount in dollars) 1100 1210 1331
option 2 (amount in dollars) 1100 1200 1300
Part B: write one function for each option to desdcribe the value of the investment f(n), in dollars, after n years
In this case, x represents the amount that has increased year after year.
What is meant by monetary value?The monetary value of an asset or service is the amount that would be paid in cash if it were sold to a third party. Tangible property, intangible property, labor, and commodities, for example, are priced at their monetary value.
Given,
Belinda wishes to invest $1,000. The table below shows the value of her investment for three different years under two different scenarios:
The number of years is 1 2 3
Option 1 (dollar amount) 1100 1200 1300
Option 2 (dollar amount) 1100 1210 1331
Part A: Using options 1 and 2, linear and exponential functions can be used to describe the value of an investment after a set number of years.
In the case of Option 1, the linear function can be used to describe the investment's value after a set number of years. This is due to the fact that in Option One, the amount increases by a fixed amount each year.
In the case of option 2, the exponential function can be used to calculate the value of the investment after a specified number of years. This is because the amount increase in Option 2 is greater than last year.
Part B: (n=n+100) and (n=n+100x) are functions for each option that describe the monetary value of the investment f(n) after n years.
Option 1's function is n = n + 100.
Option 2's function is n = n + 100 x.
In this case, x represents the amount that has increased year after year.
Part C: Yes, the value of Belinda's investment after 20 years will differ by 1900 if she chooses Option 2 over Option 1.
After 20 years, the option 1 amount would be 3000, and the option 2 amount would be 4900. As a result, there is a difference of 1900.
The complete question is:
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
To learn more about monetary value, refer to:
https://brainly.com/question/17750211
#SPJ9
I'm having problem solving these two equations I will include a picture
Given:
1) The equation is,
[tex]4x^3-5x^2-196x+245=0[/tex]To solve this equation,
using synthetic division,
Now solving further,
[tex]\begin{gathered} 4x^3-5x^2-196x+245=(x-7)(4x^2+23x-35) \\ take,\text{ }4x^2+23x-35=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{}=\frac{-23\pm\sqrt{23^2-4\cdot\:4\left(-35\right)}}{2\cdot\:4} \\ x=\frac{-23\pm\:33}{2\cdot\:4} \\ x_{}=\frac{-23+33}{2\cdot\:4},\: x_{}=\frac{-23-33}{2\cdot\:4} \\ x=\frac{5}{4},\: x=-7 \end{gathered}[/tex]Hence, the solution of given equation is,
[tex]\begin{gathered} 4x^3-5x^2-196x+245=(x-7)(x-\frac{5}{4})(x+7) \\ \Rightarrow(x-7)(x-\frac{5}{4})(x+7)=0 \\ \Rightarrow x=\text{ 7,-7,}\frac{5}{4} \end{gathered}[/tex]2) the equation is,
[tex]9x^3+2x^2+9x+2=0[/tex]Now, factor the equation,
[tex]\begin{gathered} 9x^3+2x^2+9x+2=0 \\ x^2(9x+2)+(9x+2)=0 \\ (9x+2)(x^2+1)=0 \\ \Rightarrow9x+2=0,x^2+1=0 \\ \Rightarrow x=\frac{-2}{9}, \\ \text{and x}^2=-1 \\ x=\pm\sqrt[]{-1} \\ x=\pm i \end{gathered}[/tex]Hence, the solution of above equation is x= -2/9 , i , -i.
8
Find the arc length of the partial circle.
Either enter an exact answer in terms of T or use 3.14 for T ar
units
?
▷
Relating circumference and are
The semicircle's arc measures five units. In order to get 15.7 units, we could also multiply 5 by 3.14.
How do you figure out the semicircle's arc length?a symmetrical, curved structure that spans an aperture and often bears the weight of a wall, roof, or bridge.
A semicircle is the circumference or half of a circle.
The circle's radius is r=d+h=s22h+h2. The length of the entire arc is equal to the angle of the half-arc, which is equal to arc sin(s/r) or, alternatively, arctan(s/d). Multiply this angle (in radians! ), by 2r.
The half of a circle is called a semicircle.
To learn more about arc length of a semicircle refer to:
https://brainly.in/question/3222319
#SPJ13
Represent the following sentence as an algebraic expression, where "a
number" is the letter x. You do not need to simplify.
7 is subtracted from the cube of a number.
The expression of the statement is x³ - 7
How to determine the representation of the statement?The statement is given as
7 is subtracted from the cube of a number.
Represent the number as x
So, we have the following representation
"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from the cube of x
The cube of x can be represented as x^3
So, we have
"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from x³
"7 is subtracted" means minus 7
So, we have
"7 is subtracted from the cube of a number" ⇒ x³ minus 7
Rewrite as
"7 is subtracted from the cube of a number" ⇒ x³ - 7
Hence, the expression is x³ - 7
Read more about expression at
https://brainly.com/question/723406
#SPJ1
How does the graph of f(x) = 3 cos(½x)-5 differ from the graph ofg(x) = 3 cos(x) - 5 ?A. The graph of f(x) is compressed horizontally.B. The graph of f(x) is compressed vertically.C. The graph of f(x) is stretched vertically.O D. The graph of f(x) is stretched horizontally.
Answer:
D. The graph of f(x) is stretched horizontally.
Explanation:
Given the parent function g(x) defined as follows:
[tex]g\mleft(x\mright)=3cos\mleft(x\mright)-5[/tex]If we stretch g(x) horizontally by 2, we have the function:
[tex]f(x)=3\cos (\frac{1}{2}x)-5[/tex]The correct choice is D.
Please help me with all I’ll mark you brainly
Part a: The correct solution was found by Justin as b = -1.
Part b: The mistake made by the Christian was taking negative value as positive.
What is termed as the distributive property?The distributive property too is referred to as the distributive law of addition and subtraction. The name suggests that the operation entails dividing or transferring something. According to the distributive property, an expression in the form A × (B + C) can be settled as A × (B + C) = AB + AC. This distributive law applies to subtraction as well and is written as A (B - C) = AB - AC. This means that operand A is shared with the other two operands.For the following question,
The solution found by Justin is b = 1.
The solution found by Christian is b = -1.
The equation is given as;
10(1 + 3b) = -20
To find the solution, use distributive property.
10×1 + 10×3b = -20
30b = - 20 - 10
30b = -30
b = -1
Part a: The correct solution was found by Justin as b = -1.
Part b: The mistake made by the Christian can be that he did not consider the right hand value as negative and put it as positive value.
To know more about the distributive property, here
https://brainly.com/question/24715502
#SPJ13
One side of a triangle is 5 m longer than the second side the third side is four times the length of the second side if the perimeter of the triangle is 65 m how long is the second side
10 m
Explanation:
Data:
Second side : x
Third side : four times the second side : 4*x
The other side : 5 m longer than the second side : 5 + x
Perimeter of the triangle : 65 m
Formula:
Perimeter of a triangle = one side + second side + third side
Solution:
65 = 5 + x + x + 4 * x
65 = 5 + 6 * x
65 - 5 = 5 + 6 * x - 5
60 = 6 * x
60 / 6 = 6 * x / 6
10 = x
Which of the statements below is true for the following set of numbers?20, 15, 50, 85, 75, 60a) The range is 85 and the midrange is 55.b) The range is 70 and the midrange is 35.c) The range and the midrange are equal.d) The range is 70 and the midrange is 50.
RANGE
The range of a given data is the difference between the largest and smallest numbers.
Steps for solving range:
Step 1: Arrange the data values in ascending order
[tex]\Rightarrow15,20,50,60,75,85[/tex]Step 2: Identify the largest and smallest numbers
[tex]\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}[/tex]Step 3: Calculate the difference between the numbers.
[tex]\begin{gathered} Range=Largest-Smallest \\ \therefore \\ Range=85-15=70 \end{gathered}[/tex]The range is 70.
MIDRANGE
The midrange of a given set of data is the average of the largest and smallest number.
Steps for solving midrange:
Step 1: Arrange the data values in ascending order
[tex]\Rightarrow15,20,50,60,75,85[/tex]Step 2: Identify the largest and smallest numbers
[tex]\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}[/tex]Step 3: Calculate the average of the numbers.
[tex]\begin{gathered} Midrange=\frac{Largest-Smallest}{2} \\ \therefore \\ Midrange=\frac{85-15}{2} \\ Midrange=\frac{70}{2} \\ Midrange=35 \end{gathered}[/tex]The midrange is 35.
ANSWER:
The correct option is OPTION B.
Raina wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 7.8% interest, compounded quarterly. Payments will be made at the end of each quarter
How much money will she need to pay into the annuity each quarter for the annuity to have a total value $5,000 after 3 years ?
Round your final answer to the nearest cent
AS per the compound interest, She need to pay $110.59 into the annuity each month for the annuity to have a total value of $5000 after 3 years.
Compound interest:
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
It differs from simple interest, where as the interest is not added to the principal while calculating the interest during the next period.
Given,
Raina wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 7.8% interest, compounded quarterly.
Payment will made each quarter.
Here we need to find the amount she need to pay into the annuity each quarter for the annuity to have a total value $5,000 after 3 years.
Here we know that,
Total value of annuity after 3 years = $5,000
Interest rate = 7.8% = 0.078 compounded quarterly.
Number of year = 3 years
First, convert R as a percent to r as a decimal
r = R/100
r = 7.8/100
r = 0.078 per year,
Then, solve the equation for P
P = A / (1 + r/n)ⁿˣ
P = 5,000.00 / (1 + 0.078/4)(4)(3)
P = 5,000.00 / (1 + 0.0195)(12)
P = $3,965.73
We know that, 3 years = 36 months.
So for one moth she need to pay,
Monthly pay = $3,965.73/36 = $110.59
To know more about Compound interest here.
https://brainly.com/question/14295570
#SPJ1
the cost of a ticket to the circus is 21.00 for children and 36.00 for adults on a certain day attendance at the circus was 19,000 and the total gate revenue was 56,400 how many children and how many adults bought tickets?the number of children was______The number of adults was____
We know that
• The ticket for children costs $21.
,• The ticket for adults costs $36.
,• There were 19 people.
,• The total gate revenue is $56,400.
To solve this we have to form a system of linear equations. The first equation would be
[tex]x+y=1,900[/tex]Where x is children and y is adults, there were 19 in total.
The second equation would be
[tex]21x+36y=56,400[/tex]This equation represents the total earnings.
Let's isolate y in the first equation.
[tex]y=1,900-x[/tex]Now, we replace this expression in the second equation.
[tex]\begin{gathered} 21x+36(1,900-x)=56,400 \\ 21x+68,400-36x=56,400 \\ -15x=56,400-68,400 \\ -15x=-12,000 \\ x=\frac{-12,000}{-15} \\ x=800 \end{gathered}[/tex]There were 800 children.Then, we use this value to find y.
[tex]\begin{gathered} y=1,900-x \\ y=1,900-800 \\ y=1,100 \end{gathered}[/tex]There were 1,100 adults.Therefore, the number of children was 800, and the number of adults was 1,100.Try AgainYour answer is incorrect.Raina has a rectangular poster that is 20 centimeters long and17 centimeters wide. What is the area of the poster in squaremeters? Do not round your answer.0m²XSConversion facts for length- 1 meter (m)=1 meter (m)1000 millimeters (mm)100 centimeters (cm)10 decimeters (dm)1 decameter (dam)1 hectometer (hm)1 kilometer (km)=-==1 meter (m)10 meters (m)100 meters (m)1000 meters (m) I need help with this math problem.
To figure out the answer, the given parameters have to be converted to meters.
The conversion from centimeters to meters is given to be:
[tex]100\text{ cm}\to1\text{ m}[/tex]Therefore, the parameters are converted by dividing by 100 as shown below:
[tex]\begin{gathered} length=20\text{ cm}\div100=0.2\text{ m} \\ width=17\text{ cm}\div100=0.17\text{ m} \end{gathered}[/tex]Hence, the area of a rectangle formula can be applied:
[tex]area=length\times width[/tex]Substituting known values, the area is calculated as shown below:
[tex]\begin{gathered} area=0.2\times0.17 \\ area=0.034 \end{gathered}[/tex]The area is 0.034 m².
A line passes through the point (-1, -6) and has a slope of -5.
Write an equation in point-slope form for this line.
The linear equation with a slope of -5 and that passese through (-1, -6) is:
y = -5*x - 11
How to write the equation of the line?A general linear equation is of the form:
y = a*x +b
Where a is the slope and b is the y-intercept, here we know taht the slope is -5, then:
y = -5*x + b
Now we also know that the line passes through (-1, -6), then we can replace that to get:
-6 = -5*-1 + b
-6 = 5 + b
-6 - 5 = b
-11 = b
Then the linear equation is:
y = -5*x - 11
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
The difference of two numbers is
2
. Two times the smaller is
8
more than the larger. Find the two numbers.
Answer:
10 & 12
Step-by-step explanation:
First, we set up equations:
x - y = 2
2(y) = x + 8
Then, we solve for the variable of our choice (x) in one equation:
(x - y = 2) = (x = y + 2)
Then, we substitute it for the variable (x) in the other equation:
(2y = x + 8) = (2y = (y + 2) + 8)
Then, we solve for the remaining variable (y):
(2y = (y + 2) + 8) = (2y = y + 10) = (y = 10)
Finally, we can plug the value that variable (y) into the initial equations:
(x - (10) = 2) = (x = 12)
(2(10) = x + 8) = (x = 12)
Now, we have the value of both variables:
y = 10 & x = 12
Hope this helps! Brainliest would be nice, if you can, but if not that's fine too!
using the formula above, find the surface area of a cube whise sides are all two thirds inches
Given:
The sides of the cube is, s=2/3 inches.
The objective is to find the surface area of cube.
The surface area can be calculated as,
[tex]\begin{gathered} SA=6s^2 \\ =6(\frac{2}{3})^2 \\ =6(\frac{4}{9}) \\ =2.667in^2 \end{gathered}[/tex]Hence, the surface area of the cube is 2.667 square inches.
