Answer:
The number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Explanation:
Given the equation;
[tex]x^2+2x+7=21[/tex]Let us subtract 21 from both sides;
[tex]\begin{gathered} x^2+2x+7-21=21-21 \\ x^2+2x-14=0 \end{gathered}[/tex]We can now solve for x using the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]from the equation;
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-14 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(1)(-14)}}{2(1)} \\ x=\frac{-2\pm\sqrt[]{4+56}}{2} \\ x=\frac{-2\pm\sqrt[]{60}}{2} \end{gathered}[/tex]so, we have;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{60}}{2} \\ x=\frac{-2+\sqrt[]{60}}{2} \\ x=2.87 \\ \text{and} \\ x=\frac{-2-\sqrt[]{60}}{2} \\ x=-4.87 \end{gathered}[/tex]Therefore, the number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]6x50 hundreds= 300 hundreds
The given expression 6 x 50 hundreds = 300 hundreds is true.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
⇒ 6 x 50 hundreds = 300 hundreds
Now,
Solve the expression for checking the expression is true or not as;
The expression is,
⇒ 6 x 50 hundreds = 300 hundreds
Since, The value of 6 x 50 hundreds is find by multiplying the number,
⇒ 6 x 50 hundreds = 300 hundreds
Thus, The given expression 6 x 50 hundreds = 300 hundreds is true.
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For each relation decide whether or not it’s a function(this is one problem I do an online math program with this is considered one problem)
Answer: According to the definition, the function is a relationship between two sets of numbers that matches numbers from one set to another:
Diagram for the Illustration:
Do note! That the single input can not have two outputs.
Therefore the answer is:
[tex]\begin{gathered} \text{ Relation \lparen1\rparen}\rightarrow\text{ Not a Function} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \end{gathered}[/tex][tex]\begin{gathered} \text{ Relation \lparen1\rparen}\rightarrow\text{ Not a Function} \\ \\ \text{Relat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen}\operatorname{\rightarrow}\text{Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on3}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Funct}\imaginaryI\text{on} \\ \\ \text{Relat}\imaginaryI\text{on\lparen4}\operatorname{\rparen}\operatorname{\rightarrow}\text{ Not a Funct}\imaginaryI\text{on} \end{gathered}[/tex]Or the relation(2) and (3) are functions, and the rest are not functions.
Which equation shows the relationship between X, the number of minutes and y, the price
The equation that shows the price to rent a scooter for any number of minutes will be D. y=0.15x
How to compute the equation?It is illustrated that the price of the scooter rental is $0.15 per minute. Therefore, 1 minute = $0.15
Jana rented a scooter for $60 minutes. This will be:
= 0.15 × 60
= $9
To frame an equation that shows the price to rent a scooter for any number of minutes :
Let us take,
The variable 'y' = the total price.
The variable 'x' = number of minutes for rental.
Total price = price of rent per minute × any number of minutes
y = 0.15 × x
y = 0.15x
Therefore, the appropriate equation is y = 0.15x.
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City scooters charges customers by the minute to rent an electric scooter. Jana rented a scooter for $60 minutes and paid $9. Write an equation that shows the price to rent a scooter for any number of minutes
The price of the scooter rental is $0.15
A: x=9y
B: y=9x
C: x=0.15y
D: y=0.15x
Answer: y=0.15x
Step-by-step explanation:
I ready
HELP ASAP
Simplify −6g(3g + 2).
−18g2 + 2
−18g2 − 12g
−18g + 2
−18g − 12g
The simplified form of the expression -6g(3g+2) is option (D) [tex]-18g^2-12g[/tex]
The expression is
-6g(3g+2)
The distributive property states that the multiplying the sum of two or more variables by a number will give the same answer as multiplying each variables individually by the number and then adding the products together.
The distributive property of addition is
A(B + C) = AB + AC
The distributive property of subtraction is
A(B - C) = AB - AC
Here the expression is
-6g(3g+2)
Apply the distributive property in the expression
-6g(3g+2) = (-6g) ×3g + (-6g)×2
Multiply it
= [tex]-18g^2-12g[/tex]
Hence, the simplified form of the expression -6g(3g+2) is option (D) [tex]-18g^2-12g[/tex]
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Answer:
−18g^2−12g
Step-by-step explanation:
got it right on the quiz
Write a simplified expression for the area of a rectangle with a length of (-3x - 4) and a width of (-9). Remember, Area = length x width
Area = length x width
Lenght: -3x-4
Width : -9
Replace the values of length and width in the area formula:
Area: (-3x-4) (-9)
Apply distributive property:
A = -3x(-9)+ (-4)(-9)
A = 27x+36
A laptop computer is purchased for $3200. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.
we know that
Each year, its value is 80% of its value the year before
that is the same as
Each year the value decreases by 20%
we have an exponential decay function of the form
[tex]y=a(1-r)^x[/tex]where
y is the value of the computer laptop
x is the number of years
r is the rate
a is the initial value
so
we have
a=$3,200
r=20%=20/100=0.20
substitute
[tex]\begin{gathered} y=3,200(1-0.20)^x \\ y=3,200(0.80)^x \end{gathered}[/tex]For y=$700
substitute in the equation above
[tex]\begin{gathered} 700=3,200(0.80)^x \\ solve\text{ for x} \\ \frac{700}{3,200}=(0.80)^x \end{gathered}[/tex]Apply log on both sides
[tex]\begin{gathered} log(\frac{700}{3,200})=x*log(0.80) \\ x=6.81\text{ years} \end{gathered}[/tex]therefore
The answer is 7 yearsHelp with finding proofs
Answer:
Statement: ∠XYZ = ∠ABC Reasons: Below
Step-by-step explanation:
For two angles to be complementary means that the sum of the two angles is equivalent to 90°. When an angle has one of those little squares, that means the angle is a right angle, or a 90° angle. Also, since it's given that line segment AB and line segment BC are perpendicular, this means the two lines/line segments cross each other at a right angle, which also proves that line segment AB and BC have a 90° angle.
These triangles are scaled copies of each other. Triangle G has area of 6. Triangle B has area of 1.5. How many times larger if the area of Triangle B than Triangle G
The area of triangle G is 4 times the area of triangle B.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Triangles G and B are scaled copies of each other.
The area of Triangle G is 6 and the area of triangle B is 1.5.
Let x be the number by which the area of triangle G is greater than the area of triangle B.
So,
area of triangle G = x times Triangle B
6 = 1.5x
x = 6/1.5
x = 4
The area of triangle G is 4 times greater than the area of triangle B.
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Jamal is 8 years older than Autumn. In 2 years the sum of their ages will be 70. How old is Jamal now?
We know that
• Jamal is 8 years older than Autumn.
,• In 2 years the sum of their ages will be 70.
Each statement above has to be expressed as an equation. Notice that "8 years older" means +8. So, the equation about the first statement is
[tex]J=A+8[/tex]Now, "in 2 years" means we have to add 2 units to each age, also we have to add them to get 70. The equation about the second equation is
[tex](A+2)+(J+2)=70[/tex]We reduce like terms
[tex]A+J+4=70[/tex]Then, we subtract 4 on each side
[tex]\begin{gathered} A+J+4-4=70-4 \\ A+J=66 \end{gathered}[/tex]Now, we replace the first equation into the last one above.
[tex]\begin{gathered} A+A+8=66 \\ 2A+8=66 \end{gathered}[/tex]We subtract 8 on each side
[tex]\begin{gathered} 2A+8-8=66-8 \\ 2A=58 \end{gathered}[/tex]At last, we divide the equation by 2
[tex]\begin{gathered} \frac{2A}{2}=\frac{58}{2} \\ A=29 \end{gathered}[/tex]Therefore, Autumn is 29 years old.Let's find Jamal's age.
[tex]J=29+8=37[/tex]Therefore, Jamal is 37 years old.Find the following quotient:
10r³ - 2x² + 8x
2x
The quotient of the expression (10x³ - 2x² + 8x)/2x is (5x² - x + 4).
What is meant by the term factorization?A polynomial can be published as the product of the its factors with degrees below or equal to the degree of the original polynomial. Factorization of polynomials refers to the process of factoring.The basic technique for factoring polynomials is to find the greatest common factor, which simplifies the problem.The second factoring technique is known as grouping. If there is no factor common to all of the terms of the a polynomial, but there are factors common to a few of the terms, this method is used.The given expression is;
= (10x³ - 2x² + 8x)/2x
Take 2x common on the numerator.
= 2x(5x² - x + 4)/2x
Cancel 2x from the numerator and denominator part.
= 5x² - x + 4
Thus, the quotient of the expression is found as 5x² - x + 4.
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There are 96 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 1/8 of the remaining houses were sold. How many houses are left to be sold?
Using the given fractions we can say that there are 56 houses left to be sold.
A fraction, which also denotes a component of a whole, or a ratio is any number divided into equal parts. When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size.
1/3 of 96 were sold...
number of houses sold = 1/3 × 96 = 96/3 = 32
So the first month 32 houses were sold.
Number of houses left = 96 - 32 = 64 houses.
number of houses sold next month = 1/8 × 64 = 64/8 = 8
8 houses were sold the second month
number of houses left 64 - 8 = 56
Therefore using the fractions 56 houses were left to be sold.
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Alison had lost some puzzle pieces. She found 3/10 of them under the coffee table and another 4/10 of them under the couch. How much is she still missing?
The fractional part that Alison is still missing is 3/10.
What is a fraction?A fraction is a part of an absolute value or number.
Fractions are always less than one.
Fractions are denoted by a numerator (upper part or dividend) less than the denominator (the lower portion known as the divisor).
There are proper and improper fractions.
The fraction found under the coffee table = 3/10
The fraction found under the couch = 4/10
The total fractional part found so far = 7/10 (3/10 + 4/10)
The fractional part that Alison misses = 3/10 (1 - 7/10)
Thus, Alison still misses 3/10, which is fractionally 30% of the puzzle pieces.
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Distance travelled = rate (or speed) * time.If Julio drives 248 miles at a constant speed of 62 mph. How long will it take? (Be sure to includeunits.)
Using the given formula:
[tex]D=s\cdot t,[/tex]substituting D=248 miles and s=62 mph, we get:
[tex]248\text{miles}=62\text{mph}\cdot t\text{.}[/tex]Dividing by 62 mph we get:
[tex]\frac{248\text{miles}}{62\text{mph}}=4\text{hours.}[/tex]Therefore, it will take 4 hours.
Answer: 4 hours.
Valentino's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust
Number Sold
Thin crust
299
Thick crust
228
Stuffed crust
168
Pan style
199
Based on this information, of the next 3000 pizzas he sells, how many should he expect to be stuffed crust? Round your answer to the nearest whole number.
Do not round any intermediate calculations.
Valentino's Pizzeria should anticipate selling 563 Stuffed crust pizza.
What is termed as the probability?The term "probability" refers to the likelihood of a specific event (or set of events) occurring, demonstrated on a linear scale from 0 (impossibility) to 1 (certainty), as well as as a percentage between 0 and 100%. Statistics is the study of events controlled by probability.The data for the type of crust on the pizza and the number of pizzas sold are given.
Thin crust: 299
Thick crust: 228
Stuffed crust: 168
Pan style: 199
Total pizza = 299 + 228 + 168 + 199
Total pizza = 894
The frequency with which a Stuffed crust pizza is sold = 168/894 = 28/149.
As a result, if Valentino's Pizzeria sells 3000 pizzas, this same expected number of Stuffed crust pizza sold is calculated by the given formula.
Number of Stuffed crust pizza Sold = Purchase Frequency of Stuffed crust pizza X Total Sales.
= 28/149 × 3000
= 563.75
= 563 pizza.
Thus, Valentino's Pizzeria should anticipate selling 563 Stuffed crust pizza.
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If there are 28 apples and 42 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
Answer:
28:42
12:21
4:7
Step-by-step explanation:
To get 12:21, divide both numbers by two
To get 4:7, divide 12:21 by 3
Answer:
28:42, 21:14, 7:10.5, 56:84
There are a lot more, but for the basics of ratios you only need to know this:
- The order is very important in the ratio, whatever number came first stays in that order.
- You can only multiply or divide the same numbers. For instance, if the ratio was 1:2, you would multiply or divide the numbers by the same number.
- When you multiply or divide the ratio/numbers, you cannot not only do whole numbers, but also decimals like 0.25 or mixed decimals like 1.5.
- Remember numbers are infinite, so you can multiply or divide your ratio/numbers by any decimal or number.
Hope this helps! :D
If the events have the same chance of happening then they are called what
Answer:
[tex]Equally\text{ Likely Events}[/tex]Explanation:
Here, we want to get the word to describe events that have the same probability
When two events have the same or equal probabilities, we say that the events have the same likelihood
The term used to describe such events are equally likely events
This table shows a function.
(-16, -41)
(-15, -20)
(-7, -2)
(-5, 5)
(2, 1)
(13, 10)
What is the average rate of change over the interval 2 ≤ x ≤ 137
A. -11/9
B. -9/11
C. 9/11
D. 11/9
Answer: Choice C) 9/11
========================================================
Explanation:
Finding the average rate of change over the interval 2 ≤ x ≤ 13 is the exact same as finding the slope of the line through the points (2,1) and (13,10)
[tex](x_1,y_1) = (2,1) \text{ and } (x_2,y_2) = (13,10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{10 - 1}{13 - 2}\\\\m = \frac{9}{11}\\\\[/tex]
The slope of the line through (2,1) and (13,10) is 9/11 which is also the rate of change we're looking for.
I don't really know what to do! could you help me!
1/36
1) Since the total number of outcomes are 36 combinations:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
2) And the question wants us to find the probability of rolling two 2s, so let's bold this combination below:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So, we can see that there is only 1 favorable outcome. Then we can write out the following quotient:
[tex]P(\text{roll) =}\frac{\text{favorable outcome}}{\text{total outcomes}}=\frac{1}{36}[/tex]3) Hence, the answer is 1/36
Round the number to the place of the underlined digit. 4.3186 (the underline number is one). The rounded number is?
Let's begin by listing out the information given to us:
The number is 4.3186
We are to round the number to the place of the underlined digit
The underlined number is 1 (the hundredth place value)
If the number after 1 is less than 5, we round down & if the number is 5 or more, we round up. The number after 1 is 8 (greater than 5). We have:
[tex]4.3186\approx4.32[/tex]Hence, the rounded number is 4.32
if f(x)=x^2+4x-3 then what is the remainder when f(x) is divided by x-3?
The remainder, R(3) = 18
Explanations:The given function is:
[tex]f(x)=x^2\text{ + 4x - 3}[/tex]According to the remainder theorem, the remainder when the function f(x) is divided x-3 is gotten by substituting x = 3 into f(x)
[tex]\begin{gathered} f(3)=R(3)=3^2+4(3)-3 \\ f(3)\text{ = R(3) = 9 + 12 - 3} \\ f(3)\text{ = R(3) = 18} \end{gathered}[/tex]The remainder = 18
Order the steps to find the inverse. Like what is step 1 then 2 then 3 then 4
In order to find the inverse of a function, the first step is "replace f(x) with y".
Then, the second step is "swap x and y".
The third step is "solve for y".
And finally, the fourth step is "change y to f^-1(x)".
For example, let's find the inverse function of f(x) = 2x:
[tex]\begin{gathered} f(x)=2x \\ y=2x \\ x=2y \\ y=\frac{x}{2} \\ f^{-1}(x)=\frac{x}{2} \end{gathered}[/tex]Determine which set of side measurements could be used to form a right triangle.
9, 11, 13
6, 12, 17
square root of 8, 5, square root of 17
square root of 2, square root of 7, 9
There is no set of sides used to form a right triangle.
Right triangle:
The one angle is always 90° or the right angle. The side opposite angle of 90° is the hypotenuse. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°.
Let a = height of a triangle
b = base of a triangle
c = hypotenuse of a triangle
So we have formula for right triangle:
c² = a² + b²
So from this, we have
a)a = 9, b = 11, c= 13
13² = 9² + 11²
169 = 81 + 121
169 ≠ 202
Therefore the side given is not a right triangle.
b) 6, 12, 17
17² = 6² + 12²
289 = 36 + 144
289 ≠ 180
So the side given is not of a right angle triangle.
c) 8, 5, 17
17² = 8² + 5²
289 = 64 + 25
289≠ 89
So the given side is not of a right angle triangle.
d) 2, 7, 9
9² = 2² + 7²
81 = 4 + 49
81 ≠ 53
So the given triangle is not a right angle triangle.
Therefore all the given option is not of a right angle triangle.
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If T(x, y) = (x + 5, y + 6) and Pris the image of P, what is the rule for the translation in which P is the image of P'? T(x, y) = (x – [?], y -[]) Enter the number that belongs in the green box. Enter
Answer:
The translation is;
[tex]T(x,y)=(x-5,y-6)[/tex]Explanation:
Given the translation rule;
[tex]T(x,y)=(x+5,y+6)[/tex]when P' is the image of P.
For the inverse, when P is the image of P', the Translation rule would become;
[tex]\begin{gathered} x=x^{\prime}+5 \\ x^{\prime}=x-5 \\ y=y^{\prime}+6 \\ y^{\prime}=y-6 \\ So,\text{ the translation rule becomes;} \\ T(x,y)=(x-5,y-6) \end{gathered}[/tex]The translation is;
[tex]T(x,y)=(x-5,y-6)[/tex]F(x-3)=x^2-1. F(0)=?
The answer is f(x−3)=x2
Write a polynomial function of least degree with real coefficients in standard form that has the given zeros.–2, –4, –3 + 4i x2 + 6x + 8x4 + 12x3 + 198x + 200x4 + 12x3 + 69x2 + 198x + 200x4 + 69x2 + 198x + 200
Write the polynomial function of least degree with real coefficients in standard form:
According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.
–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.
If c is a zero of p(x), then (x-c) is a factor of p(x).
–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.
Let the required polynomial be p(x), so
[tex]\begin{gathered} p(x)=(x+2)(x+4)(x-3+4i^2)(x+3+4i^2)_{} \\ P(x)=(x^2+2x+4x+8)(x+3)^2-(4i^2)^2) \\ (a^2-b^2)=(a-b)(a+b) \\ p(x)=x^2+6x+8)(x^2+6x+9-16i^2 \\ i^2\text{=-1} \\ p(x)=(x^2+6x+8)(x^2+6x+9-16(-1) \\ p(x)=(x^2+6x+8)(x^2+6x+9+16^{} \\ p(x)=(x^2+6x+8)(x^2+6x+25) \end{gathered}[/tex][tex]\begin{gathered} p(x)=(x^2+6x+8)(x^2+6x+25) \\ p(x)=x^2(x^2+6x+8)+6(x^2+6x+8)+25(x^2+6x+8) \\ p(x)=x^4+12x^3+69x^2+198x+200 \end{gathered}[/tex]
Combining like terms, we get
Therefore, the required polynomial is x^2 + 12x^3 +69x^2 + 198x + 200
Hence the correct answer is Option C
If f(x) = 8 - 10x and g(x) = 5x + 4, what is the value of (fg)(-2)?
O-196
O -168
022
O 78
Answer:
-168
Step-by-step explanation:
f(-2) = 8-10(-2)
f(-2) = 28
g(-2) = 5(-2)+4
g(-2) = -6
28(-6) = -168
Evaluate each expression if r=1, s=3, 1=3, and u=10. tu-3r
Explanation:
The expression: tu - 3r
where r=1, s=3, t=3, and u=10
[tex]\begin{gathered} =\text{ 3(10) - 3(1)} \\ =\text{ 30 - 3 } \\ =\text{ 27} \\ tu\text{ -3r = 27} \end{gathered}[/tex]could someone please help me with math I'm lost <3
D is not the midpoint of line BG (false)
E is the midpoint of line AI (True)
M coordinates = (-1, 4)
M coordinates = (7, -3.5)
Explanation:
1) Distance or length of line BG = 5
The mid point is the point between them. The midpoint is the #rd number between line BG.
And the 3rd number is E not D.
Hence, D is not the midpoint of line BG (false)
2) Distance or length of line AI = 8
The mid point is the point between them. The midpoint is the 4th number between line AI.
And the 3rd number is E.
Hence, E is the midpoint of line AI (True)
3) A(1,2) and B(-3, 6)
Mid point formula:
[tex]\begin{gathered} M\text{ = }\frac{\mleft(x_1+x_2\mright)}{,2},\frac{y1_{}+y_2}{2} \\ M\text{ = }\frac{1-3}{2},\frac{6+2}{2} \\ M\text{ = -2/2, 8/2} \\ M\text{ = -1, 4} \end{gathered}[/tex]4) A(6, -5) and B (8, -2)
[tex]\begin{gathered} M\text{ = }\frac{(x_1+x_2)}{,2},\frac{y1_{}+y_2}{2} \\ M\text{ = }\frac{6+8}{2},\frac{-5-2}{2} \\ M\text{ = 14/2, -7/2} \\ M\text{ = 7, -3.5} \end{gathered}[/tex]The math teacher is buying math tools to use throughout thr year. he is planning on buying twice as many rulers as protractors. the number of calculators he is planning on buying is one quarter the number of protractors. if he buys 65 items how many of each does he buy?
Let's use the variable R to represent the number of rulers, the variable P for the number of protractors and the variable C for the number of calculators.
If the teacher will buy twice as many rulers as protractors, we have the equation:
[tex]R=2P[/tex]Then, if the number of calculators is one quarter of the number of protractors, we have:
[tex]C=\frac{P}{4}[/tex]The total number of itens is 65, so:
[tex]R+P+C=65[/tex]Using the values of R and C, we have:
[tex]\begin{gathered} 2P+P+\frac{P}{4}=65 \\ \frac{8P+4P+P}{4}=\frac{260}{4} \\ 13P=260 \\ P=\frac{260}{13} \\ P=20 \\ \\ R=2P=2\cdot20=40 \\ C=\frac{P}{4}=\frac{20}{4}=5 \end{gathered}[/tex]So the teacher bought 20 protractors, 40 rulers and 5 calculators.
Graph for y = -x– 6.
Given the linear equation;
[tex]y=-x-6[/tex]To plot the graph of this equation we need to get the corresponding values of x and y at various points;
At x = 0;
[tex]\begin{gathered} y=-0-6 \\ y=-6 \\ (x,y)=(0,-6) \end{gathered}[/tex]At x = -6;
[tex]\begin{gathered} y=-(-6)-6 \\ y=+6-6 \\ y=0 \\ (x,y)=(-6,0) \end{gathered}[/tex]We can then locate this two points on the graph then join with a straight line since it is a linear graph.
Below is the graph of the linear equation given;
