Answer:
C. 9x^2 − 6x
Step-by-step explanation:
3(x + 6x^2 − 3x − 3x^2)
According to PEMDAS, we need to simplify inside the parentheses first
3(x -3x+ 6x^2 − 3x^2)
3(-2x+3x^2)
Now we can distribute the 3 to both terms inside the parentheses
3 * -2x + 3* 3x^2
-6x + 9x^2
We normally write them in decreasing powers of x
9x^2 -6x
MATH HELP...PLz
Use inductive reasoning to find the next term in EACH sequence.
a. -6, -2, 2, 6, 10....
b. 10, 30, 90, 270, 810...
c. 17, 15, 11, 5, -3,...
a. 14, 18, 22, 26.... It is +4
b. 2,430, 7,290, 21,870..... It is x3
c. So it is going -2, -4, -6, -8 so the next one would be -10 which is -13 then -12 which is -25 and so on.
Hope this helps!
Select the two pairs of figures are similar
Answer:
1st and last group represent similar figures.
Step-by-step explanation:
We have been given a graph. We are asked to find the similar figures.
We can see that triangles in the 1st group are similar triangles as the measure of their corresponding angles are equal.
We can see that rectangle in the last group are also similar as the sides of the yellow rectangle is 2 times the sides of smaller rectangle, therefore, last pair is also similar.
Therefore, 1st and last group represent similar figures.
Simplify the expression by combining like terms. 23+6c+8d−7d−6
Answer:
17 + 6c +d
Step-by-step explanation:
To simplify the expression, we need to combine like terms
23+6c+8d−7d−6
I like to put like terms next to each other
23-6+6c+8d−7d
17 + 6c +d
23 + 6c + 8d - 7d - 6
combine like terms
= 6c + (8d - 7d) +(23 - 6)
= 6c + d + 17Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
The area of the section she wants to paint is 48 square feet.
In Euclidean Geometry, the area of a rectangle can be calculated by using this formula;
Area of rectangle = length × width
Area of rectangle 1 = 4 × 9
Area of rectangle 1 = 36 square feet.
For the area of rectangle 2, we have;
Area of rectangle 2 = 4 × 3
Area of rectangle 2 = 12 square feet.
Now, we can find the area of the figure;
Area of figure = 36 + 12
Area of figure = 48 square feet.
Complete Question:
Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
20% of miran’s allowance is 5$ how much is his total allowance?
Question
20% of miran’s allowance is 5$ how much is his total allowance?
Answer:
25 $
Step-by-step explanation:
you can solve with an equation
20 : 5 = 100 : x
x = 5 * 100 : 20
x = 25
or you can solve with an expression
5 : 20 * 100 =
25
-------------------------------
check
25 * 20% = 5
the answer is good
Nathan has two parents, four grandparents, and so on. Explain how you can write both an explicit formula and a recursive formula that represents the number of ancestors Nathan has if we go back n generations.
Answer:
Explicit formula
f(n) = 2*2⁽ⁿ⁻¹⁾
Recursive formula
f(n) = aₙ₋₁ * r
Step-by-step explanation:
Since, Nathan has two parents, four grandparents, and so on, it would form a Geometric Progression (GP) series for the number of Nathan's ancestors as below:-
2, 4, 8, 16, 32, ....
First term (a₁) = 2
Common Ratio (r) = [tex]\frac{a_{2} }{a_1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
So,
Number of ancestors of Nathan if we go back n generations = a₁r⁽ⁿ⁻¹⁾
Plugging in the values of a₁ and r, we get
f(n) = 2*2⁽ⁿ⁻¹⁾ [Explicit formula]
Now,
A geometric progression (GP) series is of the form,
a, ar, ar², ar³, ar⁴, ar⁵........
in which the first term a₁=a and other the terms are obtained by multiplying with r.
Observe that each term is r times the previous term. So, to get the [tex]n_{th}[/tex] term, we multiply [tex](n-1)_{th}[/tex] term by r.
i.e. aₙ = aₙ₋₁ * r
=> f(n) = aₙ₋₁ * r [Recursive formula]
At lunch, $60\%$ of the students selected soda while $20\%$ selected milk. If 72 students selected soda, how many students selected milk?
Answer:
24 students
Step-by-step explanation:
If 60% equals 72, then 20% would be 1/3 of 72 which is 24.
Answer:
24 students selected milk
Step-by-step explanation:
Let x be the total number of students,
Since, 60% of students selected soda,
⇒ Number of students who selected soda = 60% of x = 0.6x
According to the question,
0.6x = 72
Divide both sides by 0.6,
⇒ x = 120
Now, 20% students selected milk
Hence, the number of student who selected milk = 20% of 120 = 0.20 × 120 = 24
Can someone please help me??
You didn't specify which problems you needed and you are only allowed to submit three questions in one posting so I chose to solve 1, 3, and 5.
NOTES:
Inverse means to swap the x's and y's and solve for "y"
*********************************************************************
1. Answer: y = [tex]\frac{2x+4}{3}[/tex]
Step-by-step explanation:
y = [tex]\frac{-4+3x}{2}[/tex]
swap: x = [tex]\frac{-4+3y}{2}[/tex]
2x = -4 + 3y
2x + 4 = 3y
[tex]\frac{2x+4}{3}[/tex] = y
3. Answer: y = -3(x - 1)
Step-by-step explanation:
y = [tex]-\frac{1}{3}x[/tex] + 1
swap: x = [tex]-\frac{1}{3}y[/tex] + 1
x - 1 = [tex]-\frac{1}{3}y[/tex]
-3(x - 1) = y
5. Answer: y = [tex]-\frac{4}{9}[/tex](x - 4)
Step-by-step explanation:
y = 4 - [tex]\frac{9}{4}x[/tex]
swap: x = 4 - [tex]\frac{9}{4}y[/tex]
x - 4 = [tex]-\frac{9}{4}y[/tex]
[tex]-\frac{4}{9}[/tex](x - 4) = y
2. A forest preserve rents canoes for $18 per hour. Corey has $90 to spend. Write and solve an equation to find how many hours he can rent a canoe
Answer:
5 hours
Step-by-step explanation:
Let x be the number of hours.
18x=90
Divide by 18 on each side
x=5
Final answer:
Corey can rent the canoe for 5 hours with his $90 by setting up and solving the linear equation 18x = 90.
Explanation:
To determine how many hours Corey can rent a canoe, given that he has $90 to spend and the rental cost is $18 per hour, we can set up a linear equation. We let x represent the number of hours Corey can rent the canoe for.
The equation is simply 18x = 90, where 18 represents the hourly rental rate of the canoe and 90 represents the total amount Corey has to spend.
To solve for x, we divide both sides of the equation by 18:
18x / 18 = 90 / 18
x = 5
So, Corey can rent the canoe for 5 hours with his $90.
ILL GIVE BRAINLIEST PLEASE HELP MEEE
An elephant weighs 1.1 × pounds. A giraffe weighs 2.1 × pounds. How much more does the elephant weigh than the giraffe? A. 1.0 × pounds B. 8.9 × pounds C. 1.0 × pounds D. 8.9 × pounds
Answer: B
Step-by-step explanation:
1) First find the weight of the elephant: 1.1 * 10^4 = 11,000
2) Then find the weight of the giraffe: 2.1 * 10^3 = 2,100
3) Then subtract the weight of the giraffe from the weight of the elephant
11,000 - 2,100 = 8,900
4) And there is your answer 8.9 * 10^3 = 8,900
It is found that elephant weighs 9,000 more lb than the giraffe.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
Given that an elephant weighs 1.1 x 10⁴ and a giraffe weighs 2.1 x 10³. The weight will be estimated as below;
1.1 x 10⁴ = 11000 lb
2.1 x 10³ = 2100 lb
The difference in the weight of an elephant and the Giraffe ;
D = 11000 -2100= 9000 lb
Hence, an elephant weighs 9,000 more lb than the giraffe.
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Write the arithmetic sequence 17,20,23,26... in standard form
Answer:
an=3n+14
Step-by-step explanation:
Use the formula
an=a1+d(n−1) to identify the arithmetic sequence.
an=3n+14
The standard form of the
Explanation:An arithmetic sequence is formed by adding a constant value to each term. In this case, the first term is 17 and the common difference is 3 (since we add 3 to each term to get the next term).
The standard form of an arithmetic sequence is:
an = a1 + (n-1)d
Where:
an represents the n-th term of the sequencea1 represents the first term of the sequenced represents the common differenceLet's calculate the standard form for the given arithmetic sequence:
an = 17 + (n-1)3
So, the standard form of the arithmetic sequence 17, 20, 23, 26... is an = 17 + 3(n-1).
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John is twice as old as Bill. Greg is 7 years older than Bill. Four years ago, the sum of their ages was 55. How old is Greg?
Answer:
Greg is 67 years old.
Step-by-step explanation:
John = 2 * B
G = 7 + B
J - 4 + B - 4 + G - 4 = 55
J + B + G = 67
2B + B + 7 + B = 67
4B = 60
B = 15
J = 30
G = 22
30 + 15 + 22 = 67
67 = 67
- I.A -
The age of Greg is 31 years.
What is a linear equation?A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c.When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
Calculation:-
⇒let the actual age of Bill is X years.
four years ago the age Bill = X-4
⇒ then, the age of John is twice of Bill = 2X
four years ago age John = 2X-4
⇒Greg is 7 years older than Bill
Age of Greg = 2X+7
four years ago age Gerg = 2X+7-4
Four years ago Sum of their ages = 55
⇒ ( X-4)+(2X-4)+(2X+7-4)=55
⇒X-4+2x-4+2x+7-4=55
⇒5X=60
⇒X=12
∴age of Gerg is 2X+7
⇒2(12)+7
⇒31 years
age of bill=12 years
age of John 24 years.
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30°-60°-90° special triangle. how do I solve?
In the trinagle 30 - 60 - 90 the sides are in proportion 1 : √3 : 2.
Look at the picture.
We have:
[tex]a=2\sqrt5[/tex]
Therefore
[tex]A=2a\to A=(2)(2\sqrt5)=4\sqrt5\\\\B=a\sqrt3\to B=(2\sqrt5)(\sqrt3)=2\sqrt{(5)(3)}=2\sqrt{15}[/tex]
Answer: A = 4√5, B = 2√15The length of the base and the height of a triangle are numerically equal. Their sum is 6 less than the number of units in the area of the triangle. Find the area of the triangle.
Farmers often plant crops in circular areas because one if the most efficient watering systems for crops provides water in a circular area. Passengers takes an aerial photo of a field on which a circular crop area has been planted. He prints the photo out and notes that 2 centimeters of length in the photo corresponds to 100 meters in actual height.
1. What is the scale factor of the actual farm to the photo?
(A.) 1 to 50
(B.) 1 to 98
(C.) 1 to 56
(D.) 1 to 65
Answer:
A
Step-by-step explanation: Scale Factor is defined as a ratio between the actual figure to that of the other figure.
And as it is clearly given in the question that 2 cm of length corresponds to 100 meters so the ratio comes out to be 1:50.
So the scale factor of the actual farm to the photo is A that is 1 to 50.
The scale factor of the actual farm to the photo is 1 to 50.
To determine the scale factor of the actual farm to the photo, we can use the given information that 2 centimeters in the photo corresponds to 100 meters in actual height. Since the scale factor relates the lengths in the photo to the actual heights, we need to find the ratio of the length in the photo to the corresponding actual height. In this case, the scale factor is 2 centimeters / 100 meters, which simplifies to 1 centimeter / 50 meters. Therefore, the scale factor of the actual farm to the photo is 1 to 50.
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please help immediately
Answer:
Look Below
Step-by-step explanation:
I'm not going to do any of these, i'll just set up the equation for you to find x.
9. 75+x=90
10. x+22=180
11. x=84
12. 82+78+x=180
13. (4x+3)+(x-8)=90
14. (8x+9)+(5x+15)=180 (This was hard to read, check to see if I typed it right.)
15. 2x+4+140=180
16. 4x-13=67+2x
17. 9x+7=115
18. 12x=60
19. 4x=x+21
20. 5x+12+73=180
math help will.give brainliest
Answer:
The point ( 0,-1) is a solution.
Step-by-step explanation:
y<= (x+1) (x+5)
y>= (x-1)^2 -6
See attached graph.
To prove algebraically, put the point (0,-1) into both equations and see if it is true for both of them.
y<= (x+1) (x+5)
-1 <= (0+1) (0+5)
-1<= 1*5
-1 <=5
True
y>= (x-1)^2 -6
-1 >= (-1)^2 -6
-1 >= 1-6
-1 >=-5
True
The point is a solution
64% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
A snail can crawl 2/3 of a yard in 1/5 of an hour,how many yards can a snail crawl in 1 hour?
Answer:
2 and 1/3
Step-by-step explanation:
1 hour = 5/5 so 2/3 + 5 = 8/3
= 2 and 2/3
Hope this helps :)
3 and 1/3
2/3 ÷ 1/5 = 10/3 = 3 and 1/3
1 hour = 1 × 3 and 1/3 = 3 and 1/3
i need help, i dont like math
Answer:
#1 is -1
Step-by-step explanation:
The answer to Problem 1 is the number -1. You use PEMDAS to evaluate division first, then you subtract later.
For problem 2, we combine like terms to get this answer: -4a+b. You only add the 'a' terms together, same with the 'b' terms. Think of it like having 2 books and add on 3 more books. We can write that as 2b+3b = 5b. So we have 5 books total.
Problem 3) The answer here is 1.2n after adding n to 0.2n. Think of the first n as 1n or 1.0n
Problem 4) Divide both sides by 15 and you end up with the answer a = 2
Problem 5) Answer: 31.4 This answer is found by multiplying the diameter (10) by the approximate value for pi (3.14). The formula is C = pi*d
2/3 + 5/6
Explain how to do it
Answer:
It's simple Add the fractions, find the LCD and then combine
Exact form: 3/2
Decimal form: 1.5 Hope this helps have a nice day :)
Step-by-step explanation:
Answer:
4/6 + 5/6 = 9/6
Step-by-step explanation:
First find the least common denominator which is 6. Then add the fractions. Hope this helps.
What is the solution to 4x+5=34
Answer:
x = 7.25
Step-by-step explanation:
First you must try to get the x by itself with the 4, so, you have to subtract 5 from both sides so that the five is no longer on the side of the variable. Once you do this the equation becomes 4x = 29. Then you have to get x by itself so you then have to divide the 4 on both sides and the answer it then x = 7.25
You purchased 132.49 dollars worth of wheels and bearings for your skateboards. The shop charges 15 dollars per board to install them. The total cost is 192.49 dollars. How many skateboards will be repaired?
Answer:
Four
Step-by-step explanatio
Materials + installation = $192.49
-Materials = 132.49
Installation = $ 60.00
Installation cost = 1 skateboard/$15
No. of skateboards = 60.00 × 1/15
No. of skateboards = 4
Four skateboards will be repaired.
Which ordered pairs are on the line 3x−4y=9 ?
Select each correct answer.
(1,−32)
(−1,3)
(−5,−6)
(23,−74)
Answer:
The ordered pair that is on the line is (−5,−6)
Step-by-step explanation: You have to substitute...
Soooo....
(1,-32):
3x − 4y = 9
3(1) - 4(-32) = 9
3 + 128 = 9
131 = 9
NO
Remember, a negative times a negative becomes positive.(-1,3):
3x − 4y = 9
3(-1) - 4(3) = 9
-3 - 12 = 9
-15 = 9
NO
Remember, a negative times a positive becomes a negative.Remember, a negative plus a negative becomes a negative.(-5, -6)
3x − 4y = 9
3(-5) - 4(-6) = 9
-15 + 24 = 9
9 = 9
YES
(23, -74)
3x − 4y = 9
3(23) - 4(-74) = 9
69 + 296 = 9
365 = 9
NO
By substituting the x and y values from the given ordered pairs into the equation, we find that the only ordered pair on the line represented by the equation 3x−4y=9 is (-5,-6).
Explanation:The equation 3x−4y=9 represents a line on a coordinate plane, and ordered pairs (x, y) are points on this plane. To determine which given ordered pairs are on the line, we substitute each x and y value into the equation.
For (1,-32), the equation becomes: 3*1 - 4*(-32) = 9. This simplifies to 3 + 128, which does not equal 9, therefore (1,-32) is not on the line. For (-1,3), the equation becomes: 3*(-1) - 4*3 = 9. This simplifies to -3 - 12, which also does not equal 9, therefore (-1,3) is not on the line. For (-5,-6), the equation becomes: 3*(-5) - 4*(-6) = 9. This simplifies to -15 + 24, which equals 9. So, the ordered pair (-5,-6) is on the line. For (23,-74), the equation becomes: 3*23 - 4*(-74) = 9. This simplifies to 69 + 296, which does not equal 9, therefore (23,-74) is not on the line.
The only correct ordered pair on the line 3x−4y=9 is (-5,-6).
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In the cafeteria's refrigerator, there are 10 bottles of orange juice and 20 bottles of apple juice. What is the ratio of bottles of orange juice to bottles of apple juice in the cafeteria's refrigerator?
Answer:
1:2
Step-by-step explanation:
Because 10/20 = 1/2
Answer: 10,20
Step-by-step explanation:
Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
5x + 3y = 18
5x - 3y = 30
5x - y = 30
5x + y = 18
The equation of line CD in standard form is;
B: 5x - 3y = 30
Equation of a lineFormula for slope of line between two coordinates is;
m = (y2 - y1)/(x2 - x1)
Thus, slope of line CD is;
m = (0 - (-5))/(6 - 3)
m = 5/3
Now, equation of a line in slope intercept form is; y = mx + cc is y - intercept which is when x = 0.
Point D gives us the x-intercept because y is zero.
Thus;
0 = (5/3)(6) + c
c = -10
Thus, the equation of the line CD is;
y = (5/3)x - 10
Multiply through by 3 to get;
3y = 5x - 30
>> 5x - 3y = 30
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How can you decide which variable to solve for the first when you are solving a linear system by substitution
Answer:
The variable having largest coefficient is solved first.
Step-by-step explanation:
The variable having greater coefficient is solved first because we can substitute the value of smaller coefficient variable easily as compared to the greater one.
Because in substitution method we first substitute the value of coefficient which has smallest coefficient and as a result the coefficient with greater coefficient is solved.
Final answer:
When solving a linear system by substitution, choose the variable that is already isolated in one of the equations. Substitute the value of that variable into the other equation.
Explanation:
When solving a linear system by substitution, it is important to decide which variable to solve for first. One strategy is to choose the variable that is already isolated in one of the equations. This makes it easier to substitute the value of that variable into the other equation.
For example, consider the system:
Equation 1: x + 2y = 5
Equation 2: 3x - y = 2
In this case, Equation 1 is already isolated for x, so it would be a good choice to solve for x first. By substituting the expression for x from Equation 1 into Equation 2, you can solve for the remaining variable y. Once you have the value of y, you can substitute it back into Equation 1 to find the value of x.
A biologist is studying a certain type of algae. She starts with only 1 algae bloom and observes that the number of algae blooms triples every hour. Which equation can be used to find the number of hours, h, it will take for the population to reach 6,561 algae blooms?
Table:
# of hours || algae blooms
0 1
1 3
2 9
3 27
Answer:
6,561 = 3h
Step-by-step explanation:
The equation B) [tex]\( 6,561 = 3^h \)[/tex] determines the number of hours, c[tex]\( h \)[/tex], for the algae population to reach 6,561 blooms.
1. Identify the exponential growth formula:
[tex]\[ N = N_0 \cdot r^h \][/tex]
2. Define the given variables:
[tex]- \( N \):[/tex] Final number of algae blooms = 6,561
[tex]- \( N_0 \):[/tex] Initial number of algae blooms = 1
[tex]- \( r \):[/tex] Growth rate = 3 (since the population triples every hour)
[tex]- \( h \)[/tex]: Number of hours (this is what we need to find)
3. Substitute the given values into the formula:
[tex]\[ 6,561 = 1 \cdot 3^h \][/tex]
4. Simplify the equation:
[tex]\[ 6,561 = 3^h \][/tex]
5. Result:
The equation B) [tex]\( 6,561 = 3^h \)[/tex] can be used to determine the number of hours, [tex]\( h \)[/tex], it will take for the algae population to reach 6,561 blooms.
Complete Question:
A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a ace?
A. 1/13
B. 2/13
C. 4/13
D. 12/13
Answer:
d
Step-by-step explanation:
There are 4 cards in a standard deck. So 52-4 is 48. 48 cards are not aces then. So the ratio is 48 to 52. Which simplifies to 12 to 13. Otherwise known as 12/13
Solve -3n + 4 ≥ -8.
n ≥ 4
n ≤ 4
n ≥ -4
n ≤ -4
Answer:
n ≤ 4
Step-by-step explanation:
-3n + 4 ≥ -8.
Subtract 4 from each side
-3n + 4-4 ≥ -8-4
-3n ≥ -12
Divide by -3 on each side, remembering to flip the inequality
-3n/-3 ≤ -12/-3
n≤4
-3n + 4 ≥ -8 Subtract 4 on both sides
-3n + 4 - 4 ≥ - 8 - 4
-3n ≥ - 12 Divide -3 on both sides to get "n" by itself
n ≤ 4 (when you multiply or divide a negative number on both sides of the inequality, you flip the sign(< > ≤ ≥))
The 2nd option is your answer