Answers
The required solution of the function f(x) = -3x + 5 at x = -2 is 11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given function,
f(x) = -3x + 5
Substitute x with -2 to find f(-2).
f(-2) = -3(-2) + 5
f(-2) = +6 + 5
f(-2) = 11
Thus, the required solution of the function at x = -2 is 11.
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Related Questions
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.
Answers
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
Answers
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
Order the steps to find the inverse. Like what is step 1 then 2 then 3 then 4
Answers
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]The difference between two numbers is 22. The sum of twice the smaller number and 3 times the greater number is 246.
Answers
Given:
The difference between two numbers is 22.
The sum of twice the smaller number and 3 times the greater number is 246.
Required:
To find the two numbers.
Explanation:
Let the two numbers be x and y.
Let y be the smaller number.
The difference between two numbers is 22.
[tex]x-y=22[/tex]The sum of twice the smaller number and 3 times the greater number is 246.
[tex]2y+3x=246[/tex]Now
[tex]\begin{gathered} 2y+3(22+y)=246 \\ 2y+66+3y=246 \\ 5y=246-66 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}[/tex]Now x is,
[tex]\begin{gathered} x-36=22 \\ x=22+36 \\ x=58 \end{gathered}[/tex]Final Answer:
The two numbers are 58 and 36.
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)
Answers
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.
Five more than the product of a number and 8 equals 3 Use y for the unknown variable
Answers
Answer
y = -1/4
Step-by-step explanation:
Let the unknown variable be y
5 more than the product of a number and 8 equals to 3 can be expressed mathematically as
Recall, that the unknown variable is y
5 + (8 * y) = 3
Open the parenthesis
5 + 8y = 3
Substract 5 from both sides
5 - 5 + 8y = 3 - 5
8y = -2
y = -2/8
y = -1/4
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?
Answers
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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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?
Answers
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.
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.
Answers
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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Choose the right graph: A,B,C Or DX < -5Then write the solution interval notation
Answers
x ≤ -5
This can be written in interval notation as :
( - ∞ , -5]
The correct option is option A
Find the following quotient:
10r³ - 2x² + 8x
2x
Answers
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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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
Answers
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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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.
Answers
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 yearsif f(x)=x^2+4x-3 then what is the remainder when f(x) is divided by x-3?
Answers
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
angle ABC is a circumscribed about point H with points of tangency D,E, F what is the perimeter of a b and c? but i know AB =7 and ac+ad+dc=6+4=10 but i dont know BC and on
Answers
Answer
Perimeter = 22 units
Explanation
To answer this, we need to note that two tangents to a circle that start from the same point usually have the same lengths.
So,
AD = AE = 6
CD = CF = 4
Since,
AB = 7 and AB = AE + EB
AE = 6
So,
AB = AE + EB
7 = 6 + EB
EB = 7 - 6
EB = 1
FB = EB = 1
So,
AC = AD + DC = 6 + 4 = 10
AB = 7
CB = CF + FB = 4 + 1 = 5
So, the perimeter of the triangle is given as the sum of all its exterior sides
Perimeter = AB + AC + CB
Perimeter = 7 + 10 + 5 = 22 units
Hope this Helps!!!
Find (y + 3)(y2 + 8y – 2). (y + 3)(y2 + 8y – 2) =
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)
simplify
Step 02:
We must apply the algebraic rules to find the solution.
(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)
Part 1:
(y + 3)(y² + 8y – 2) = y³ + 8y² - 2y + 3y² + 24y - 6
= y³ + 11y² + 22y - 6
Part 2:
(y³ + 11y² + 22y - 6) * (y³ + 11y² + 22y - 6) =
[tex]y^6+11y^5+22y^4-6y^3+11y^5+121y^4+242y^3-66y^2+22y^4+242y^3+484y^2-132y-6y^3-66y^2-132y+36[/tex][tex]y^6+22y^5+165y^4+472y^3+352y^2-264y\text{ }+36[/tex]That is the full solution.
2
9
m
8
4
3
5 6
7
If l is parallel m and r parallel s explain how you know Angele 1 and Angle 6 are supplementary
Answers
Angle 4 and angle 6 are supplementary to each other.
Given : the two line r and s are parallel to each other and there are two transversals
And thus angle 6 and angle 4 are equal because angles corresponding angles are equal. This is because of a theorem which states that angles on the same side of the two parallel lines are equal .
And this further implies that the angle adjacent to angle 4 and angle form will form an angle whose sum would be equal to 180 degree. That is they will form a supplementary angle .
And this angle and angle 1 are equal because these two angles are corresponding angles and as mentioned above because of that theorem they are equal.
Thus from these two above mentioned arguments it is clear that angle 4 and angle 6 are supplementary angles .
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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?
Answers
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.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
Answers
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
d what is 38 divided by 7? Round to the nearest hundredth if necessary
Answers
HELP ASAP
Simplify −6g(3g + 2).
−18g2 + 2
−18g2 − 12g
−18g + 2
−18g − 12g
Answers
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
Answers
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
Round the number to the place of the underlined digit. 4.3186 (the underline number is one). The rounded number is?
Answers
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
simplify with like terms; 3(x - 5)
Answers
We are given the following expression:
[tex]3(x-5)[/tex]We can apply the distributive property to get:
[tex]3x-15[/tex]Since there are no like terms this expression can't be simplified any further.
could someone please help me with math I'm lost <3
Answers
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]4Solve for x given that det5 31det2-4Tха
Answers
ANSWER:
The value of x is 2
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=\det \: \begin{pmatrix}5 & 3x \\ 1 & 2\end{pmatrix}[/tex]We solve as follows:
[tex]\begin{gathered} \det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=4\cdot x-(-4)\cdot(-1)=4x-4 \\ \det \: \begin{pmatrix}5 & 3x \\ \: 1 & 2\end{pmatrix}=5\cdot2-1\cdot3x=10-3x \\ \text{therefore:} \\ 4x-4=10-3x \\ 4x+3x=10+4 \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]If f(x) = 8 - 10x and g(x) = 5x + 4, what is the value of (fg)(-2)?
O-196
O -168
022
O 78
Answers
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
6x50 hundreds= 300 hundreds
Answers
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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f(x) = 2-4
Find f(2)
Answers
Answer:
-8
Step-by-step explanation:
So first off, x is 2-4. So that's the default. It would be -2. If you multiply -2 by 2, it is -4.
Help with finding proofs
Answers
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.
