To evaluate a function at a specific x value simply means to substitute that particular value in place of every occurrence of the variable x.
So, starting from [tex] f(x) = 6x+7 [/tex], we have
[tex] f(-3) = 6\cdot(-3)+7 = -18+7 = -11 [/tex]
What is 4 * 492 equal to the product
Answer:
1968
Step-by-step explanation:
I use the following method when it comes about products of big numbers
I grab the longer and put on the first line, below I put the smallest number.
492
x 4
Now, it is time to distribute the product, term by term, remember that when performing a product, if the result is greater or equal than 10, you need to carry a number for the following product.
492
x 4
--------------------
19 6 8
(end) (c3) (nc)
nc means: not carrying anything since 4x2=8 and 8 <10
c3 means: carrying 3 since 4x9= 32 and 32 >10
end means: put the whole number and sum it what you were carrying. 4*4+3=19
The product 492*4=1968
The product of 4 multiplied by 492 equals 1968. To find this, we used a step-by-step approach using basic multiplication and the distributive property.
To determine the product of 4 multiplied by 492, you can execute the following steps:
First, break down the problem into smaller, manageable parts. Let's use the fact that 4 = 2 x 2.Multiply 4 by 492 directly: 4 × 492.To perform this calculation step-by-step, you can apply the distributive property: (4 × 500) - (4 × 8).Calculate each part: 4 × 500 = 2000 and 4 × 8 = 32.Subtract the second product from the first: 2000 - 32 = 1968.Therefore, 4 × 492 = 1968.
In a basketball game, the bulldogs make a total of 21 shots. Some of the shots are 2-pt shots while others are 3-pt shots. The bulldogs score a total of 50 points. How many 2-point and 3-point shots did they make?
Answer:
It is 8 3 pointers and 13 2 pointers
Step-by-step explanation:
8 x 3 = 24
13 x 2 = 26
24 + 26 = 50
The bulldogs made 13 2-pt shots and 8 3-pt shots.
Explanation:Let's assume that the bulldogs made x 2-pt shots and y 3-pt shots. Since each 2-pt shot is worth 2 points and each 3-pt shot is worth 3 points, we can set up the following equations: 2x + 3y = 50 (equation 1) and x + y = 21 (equation 2). To solve this system of equations, we can multiply equation 2 by 2 to get 2x + 2y = 42, and then subtract equation 1 from it. This gives us y = 8. Substituting y = 8 into equation 2, we get x + 8 = 21, which means x = 13. Therefore, the bulldogs made 13 2-pt shots and 8 3-pt shots.
Learn more about Scoring in basketball here:https://brainly.com/question/20149600
#SPJ
3/8 into a mixed number
Answer:
296
Step-by-step explanation:
111/3 = 37
37 * 8 = 296
Hope this helps :-)
calculate the midpoint of a line segment with the endpoints 7,12 and -1,6
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]A(7,\ 12)\to x_A=7,\ y_A=12\\B(-1,\ 6)\to x_B=-1,\ y_B=6[/tex]
Substitute:
[tex]\dfrac{7+(-1)}{2}=\dfrac{7-1}{2}=\dfrac{6}{2}=3\\\\\dfrac{12+6}{2}=\dfrac{18}{2}=9[/tex]
Answer: (3, 9).Simplify the expression. Write your answer as a power.
8^10⋅8^4
8^14 is the answer.
This is because since they both have the same base, the exponents could be added together if the numbers are multiplied together
Hello Tim!
[tex]8^1^0*8^4[/tex]
First you had to used apply exponent rule.
[tex]8^1^0*8^4=8^1^0^+^4=8^1^4[/tex]
[tex]=8^1^4[/tex]
Answer⇒⇒⇒8¹⁴
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
No scale is shown on this map of a wilderness area. The distance between Rose Lake and the main road is 3.5 mi. On the map it is 2 in. The distance from Rose Lake to the hiking trail is 4 in. What is the actual distance in miles between Rose Lake and the hiking trail?
Final answer:
To find the actual distance from Rose Lake to the hiking trail, a proportion is used based on the given information of the map scale, resulting in an actual distance of 7 miles.
Explanation:
The question involves solving for an actual distance on a map scale, which is a proportional relationship problem in mathematics. To find the actual distance between Rose Lake and the hiking trail, we can set up a proportion using the given distances: if 2 inches on the map equal 3.5 miles in reality, then 4 inches would represent the distance from Rose Lake to the hiking trail (since the relationship between inches on the map and actual miles should be consistent).
Set up the proportion as follows:
2 inches (map) / 3.5 miles (real) = 4 inches (map) / X miles (real)
Now, solve for X, which represents the unknown actual distance in miles. By cross-multiplying and solving for X, we get:
X = (4 inches * 3.5 miles) / 2 inches
Therefore, the actual distance between Rose Lake and the hiking trail is 7 miles.
which of the following represents this function written in standard form? y=3(x-1)(x+6)
Answer:
y = 3x^2+15x-18
Step-by-step explanation:
Parabola has an equation with one variable in degree 2 and other in degree 1.
Given that y=3(x-1)(x+6) is the function.
y is of degree 1 and x of degree 2
Standard form of these types of parabolas would be
y =ax^2+bx+c.
To make the given equation in standard form, we multiply all factors on the right side
y = 3(x-1)(x+6) = 3(x^2+5x-6)
= 3x^2+15x-18
a=3 b = 15 and c =-18
y = 3x^2+15x-18 is the standard form of the parabola
Answer:
y = 3x^2 + 15x - 18
Step-by-step explanation:
To represent the function y = 3 (x - 1) (x + 6), start by by expanding the equation by multiplying the common factor with each term inside the brackets to get:
y = 3 (x - 1) (x + 6)
y = (3x - 3) (x + 6)
Now multiply both the terms with each other to get:
y = 3x^2 + 18x - 3x - 18
Arrange the like terms together and add them:
y = 3x^2 + 15x - 18
Hence, y = 3x^2 + 15x - 18 is the standard form of the given function.
Solve for x.
−32>−5+9x
The inequality is
[tex]-32> -5+9x[/tex]
We need to isolate x and for that first we need to get rid of 5 by adding 5 to both sides.
[tex]-32+5 +-5+9x+5\\-27>9x\\[/tex]
Now we need to get rid of 9 and for that we divide both sides by 9 .That is
[tex]-\frac{27}{9}>\frac{9x}{9}[/tex]
[tex]-3>x[/tex]
[tex]x<-3[/tex]
Can someone help me with these problems
2) angles are vertical so they are congruent- 7x-27= 4x+12 --> subtract 4x from both sides so 3x-27=12 --> add 12 to both sides so 3x=39 (divide both sides by 3) so then x= 13
3) again, vertical angles so 8x-120= 4x+16 --> subtract 4x so that 4x-120=16 --> add 120 to both sides and then 4x=136, divide both by 4 and x= 34
hope this helps:))
if D is the midpoint of CE, CD =9X-7, and DE= 3X+17, find CE.
CE is equal to 58 units.
To find the length of CE, we'll use the fact that D is the midpoint of CE. The midpoint of a line segment divides it into two equal parts.
If CD is one part and DE is the other, then we can set up an equation:
CD=DE
9X−7=3X+17
Now, solve for X:
6X=24
X=4
Now that we have the value of X, substitute it back into either CD or DE to find the length of each part:
CD=9X−7=9(4) −7=36−7=29
DE=3X+17=3(4) +17=12+17=29
Now, since D is the midpoint, CD and DE are equal.
CD=DE=29
Finally, CE, the total length, is the sum of CD and DE:
CE=CD+DE=29+29=58
So, CE is indeed 58
50 times the sum of 64 and 36
(64+36)x50= 5,000
Brainliest Please
50(64 + 36) = 5000
Hope this helps
-AaronWiseIsBae
Using graph paper determine the line described by the given point and slope (0,0) and -2/3
Answer:
your graph is gonna have a horizontal line crossing the y axis at (0,3)
Heather eats a jelly sandwich every 5th day and drinks milk every 4th day. If she had a jelly sandwich and milk today, how many days will pass before she will have both again?
Follow below steps:
The question is asking to identify how many days will pass before Heather will have both a jelly sandwich and milk again, given that she eats a jelly sandwich every 5th day and drinks milk every 4th day. To find out when Heather will have both on the same day again, we need to find the Least Common Multiple (LCM) of the two numbers, 5 and 4.
The multiples of 5 are 5, 10, 15, 20, 25, and so on. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The first common multiple of both 5 and 4 is 20. Therefore, Heather will have both a jelly sandwich and milk together on every 20th day after today.
So, after today, Heather will wait 19 more days before having both a jelly sandwich and milk on the same day again.
What’s the derivative of sin^2(cos(x^2))
Answer:
[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 2 \sin (\cos x^2) \Big( \sin (\cos x^2) \Big)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin (\cos x^2) \cos (\cos x^2) (\cos x^2)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin x^2 \sin (\cos x^2) \cos (\cos x^2) (x^2)'[/tex]Basic Power Rule: [tex]\displaystyle y' = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
an industrial machine was able to make 9 pens in 3 seconds what is the rate made per second
3 pens per 1 seconds it is so easy
Simplify: 6x - 3y + 5y - 10x
Answer: -4x + 2y
Step-by-step explanation:
6x - 3y + 5y - 10 x
Group like terms:
= 6x - 10x - 3y + 5y
Add similar elements :
6x - 10 x = - 4x
- 3y + 5y = +2y
Therefore:
-4x + 2y
Hope that helps!
The simplified form of the equation [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].
Further explanation:
A binomial is an algebraic expression which consists of two terms having operations of addition and subtraction.
Procedure:
The following steps are involved to simplify the algebraic expression.
1) First we collect the like terms from the given algebraic expression.
2) Second we add or subtract the like terms in the algebraic expression.
Given:
The algebraic expression is [tex]6x-3y+5y-10x[/tex].
Calculation:
Step 1:
First we collect the like terms from the given algebraic expression.
The given algebraic expression consists two variables [tex]x[/tex] and [tex]y[/tex].
Clearly, we can see that the given algebraic expression is in the form of binomial.
So, collect the terms of [tex]x[/tex] aside and the [tex]y[/tex] term on other side as follows:
[tex]\boxed{(6x-10x)+(5y-3y)}[/tex]
Step 2:
Now, add the given algebraic expression to simplify it.
[tex]\boxed{(6x-10x)+(5y-3y)=-4x+2y}[/tex]
The above algebraic expression can be written as,
[tex]\boxed{2y-4x}[/tex]
The simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].
Thus, the simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].
Learn more:
1) Learn more about simplification of the expressions with BODMAS rule https://brainly.com/question/365957
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3) Learn more about to solve the equations for the variable https://brainly.com/question/1682776
Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Simplification
Keywords: Addition, subtraction, operation, terms, like terms, unlike terms, variables, binomial, monomial, simplification, collecting the terms, coefficient, constant, value, algebraic expressions.
Little Melinda has nickels and quarters in her bank. She has two
fewer nickels than quarters. She has $3.50
in the bank. How many coins of each type does she have?
How many quarters does she have?
A) N +2 = Q which equals
A) N -Q = -2
B) .05N +.25Q = 3.50 multiplying A) by .25
A) .25N -.25Q = -.5 then adding A) and B)
.30N = 3
Nickels = 10 Quarters = 12
*************DOUBLE CHECK ***************
.05 nickels = $0.50 .25 Quarters = $3.00
Melinda has 12 quarters and 10 nickels in her bank, totaling $3.50. By setting up and solving equations based on the values of the coins, we were able to determine the exact number of each type of coin.
Explanation:Little Melinda has nickels and quarters in her bank, with two fewer nickels than quarters. The total amount of money she has is $3.50. To determine how many coins of each type she has, we need to set up equations based on the values of the coins and the given conditions.
Let's define:
Q = number of quarters
N = number of nickels
Since each quarter is worth 25 cents and each nickel is worth 5 cents, we have the following equations:
1. N = Q - 2 (since she has two fewer nickels than quarters)
2. (5 × N) + (25 × Q) = 350 cents (because the total amount is $3.50)
Substitute the first equation into the second to find the number of each coin:
5(Q - 2) + 25Q = 350
5Q - 10 + 25Q = 350
30Q - 10 = 350
30Q = 360
Q = 12
Then, substitute Q = 12 into the first equation to find N:
N = 12 - 2
N = 10
Therefore, Melinda has 12 quarters and 10 nickels.
1. Estimate how many times larger 4 x 1015 is than 8 x 109 in the form of a single digit times an integer power of 10. 2. Estimate how many times larger 2 x 10-5 is than 4 x 10-12 in the form of a single digit times an integer power of 10.
Answer:
[tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]
[tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]
Explanation:
Ratio between [tex]4*10^{15}[/tex] and [tex]8*10^9[/tex] = [tex]\frac{4*10^{15}}{8*10^9} =5*10^5[/tex]
So [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]
Ratio between [tex]2*10^{-5}[/tex] and [tex]4*10^{-12}[/tex] = [tex]\frac{2*10^{-5}}{4*10^{-12}} =5*10^6[/tex]
So [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]
nick can read 3 pages in 1 minute. write the ordered pairs for nick reading 0,1,2, and 3 minutes.
(0, 0) 0 pages in zero minutes.
(3, 1) 3 pages in one minute.
(6, 2) 6 pages in two minutes.
(9, 3) 9 pages in three minutes.
Write the expanded form for the decimal 24.56
Final answer:
The expanded form of the decimal 24.56 is 20 + 4 + 0.5 + 0.06, which breaks down each digit by its place value.
Explanation:
The expanded form of the decimal 24.56 is an expression that shows the value of each digit in the number. To write it in expanded form, we break down each digit according to its place value. For the number 24.56, the expanded form would look like this:
20 (which represents 2 tens, or 2 × 10)4 (which represents 4 ones, or 4 × 1)0.5 (which represents 5 tenths, or 5 × 0.1)0.06 (which represents 6 hundredths, or 6 × 0.01)Combining these values, the expanded form of 24.56 is:
20 + 4 + 0.5 + 0.06
a total of $9500 is invested, part at 10% simple interest and part at 9%. if the total annual return from the two investments is $914.00, how much is invested at each rate?
a total of $9500 is invested, part at 10% simple interest and part at 9%
if the total annual return from the two investments is $914.00
Amount invested = 9500
Total amount return means total yield = $914
Let x amount is invested at 10% simple interest
Interest for first part = 10 % times x = 0.10x
Remaining part invested is 9500 -x
Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)
Total interest yield is 914. Now we frame an equation
0.10x + 0.09(9500-x) = 914
0.10x +855 - 0.09x = 914 (combine like terms)
0.01 x + 855 = 914 (subtract 855)
0.01x = 59 ( divide both sides by 0.01)
So x = 5900
$5900 is invested in 10% simple interest
9500 - 5900 = $3600 is invested in 9% simple interest
Final answer:
To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.
Explanation:
Investment Allocation Problem
Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:
x + y = 9500
The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:
0.10x + 0.09y = 914
Now we can solve the system of equations:
x + y = 9500 (Equation 1)
0.10x + 0.09y = 914 (Equation 2)
Multiplying Equation 1 by 0.10 gives us a new equation:
0.10x + 0.10y = 950 (Equation 3)
Now, we subtract Equation 2 from Equation 3:
(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914
0.10y - 0.09y = 36
0.01y = 36
y = 3600
Substitute y = 3600 into Equation 1 to find x:
x + 3600 = 9500
x = 5900
Therefore, $5900 is invested at 10% and $3600 is invested at 9%.
Please help me with this and thank you so much!
1 place to the right of a decimal point is the tenths, so you would multiply 7 by 1/10.
2 places to the right of the decimal point is the hundredths place, so you would multiply 23 by 1/100
The correct answer is D.
Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.0
Answer: 4:1
Step-by-step explanation:
Given:- Number of tables in the classroom=6
Number of students on each table = 4
thus number of students in the classroom =6×4=24 students
Now ratio of numbers of students to the tables in the classroom= numbers of students/tables in the classroom=24/6=4/1=4:1
Ratio of numbers of students to the tables in the classroom= 4:1
If 2 3 of the 12 jelly beans were eaten, how many were eaten?
2/3 x 12 = 8
8 jelly beans were eaten
You would have to multiply 2/3 and 12 to find out how many jelly beans were eaten. 2/3*12=8
Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.
Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:
•Tony's car can travel 28 miles for each gallon of gas.
•The average fuel cost at the time of their trip is $3 per gallon.
•They plan to drive about 650 miles each day.
•They estimate the average cost of a hotel each night is $85.
•They will drive approximately 2,240 miles to get from Albuquerque to Boston.
Willing to give TONS OF POINTS for this answer, remember explain how you got it.
Hello...
Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.
Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:
•Tony's car can travel 28 miles for each gallon of gas.
•The average fuel cost at the time of their trip is $3 per gallon.
•They plan to drive about 650 miles each day.
•They estimate the average cost of a hotel each night is $85.
•They will drive approximately 2,240 miles to get from Albuquerque to Boston.
Solution:
Cost of Gas:
2240 / 28 x 3 = $240
Cost of Lodging:
85 x floor2240 / 650 = $255
Cost of both: $240 +255 = $495.
The cost for a 1/4 share is $495/4 = $123.75.
What is the perimeter of the quadrilateral 9m 5m 7m 11m
The perimeter is 32m add all sides to find perimeter
the money used in eygpt is called the pound.The exchange rate is $5 to 29 pounds. Find how many Pounds you would recieve if you exchanged $15
87 Pounds would be the correct answer I believe.
5x=29x
x=3
87 pounds
Since $5 = 29. You can multiply both 5 and 29 to get 15=87 pounds
3s+6 less than or equal to -5(s+2)
3s+6 <= -5(s+2)
3s+6 <= -5s - 10
8s + 6 <= -10
8s <= -16
s <= -2
outhside High School had a big basketball game Friday night. Six players contributed to their score. Three players scored 16 points each, 2 players made 21 points each and 1 player scored 8 points. Which expression would give you their final score?
A) (16 + 21 + 8) x 6
B) 3 x 16 + 2 x 21 +1
C) (3 x 16) + (2 x 21) + 8
D) (3 + 2 + 1) x (16 + 21 + 8)
*I hope this will help*
(3 x 16) + (2 x 21) + 8
3 people made 16, which is 48
2 made 21, making 42
and 1 made 8, making 8
The answer would be c. because there is 3 players with 16 points (3x16) and 2 with 21 points (2x21) so (3x16)+(2x21) and one player scored 8 points so (3x16)+(2x21)+8
I hope this helps have a nice day
find the value of X
A x= 18
B x=22.5
C x=30
D x=54
First the two angles are equal to one another so take note of that.
Now setup the equation which will be
x+90=4x
Now get rid of alike terms
So subtract x from both sides
90=3x
Now divide 90 by 3
x=30
Answer: The correct option is
(C) x = 30.
Step-by-step explanation: We are given to find the value of x from the figure shown.
From the figure, we note that the angles with measures (x+90)° and 4x° are vertically opposite angles.
Since the measures of two vertically opposite angles are equal, so we must have
[tex](x+90)^\circ=4x^\circ\\\\\Rightarrow x+90=4x\\\\\Rightarrow 4x-x=90\\\\\Rightarrow 3x=90\\\\\Rightarrow x=\dfrac{90}{3}\\\\\Rightarrow x=30.[/tex]
Thus, the required value of x is 30.
Option (C) is CORRECT.