Answer:a)m =K n
b)m = 32
c)n=15
Step-by-step explanation:
M varies directly as n can be expressed mathematically as
m ∝ n
Introducing the constant of proportionality, K, we have that
m =K n
Now when m=14 and n=7, K becomes
14=K X 7
K=14/7 = 2
b) find m when n=16
m =K n
m = 2 x 16=32
c) find n when m=30
m =K n
30=2 x n
n=30/2 =15
Expression is formed using numbers, variables, and mathematical operations. The value of m, when the value of n is 16 is 32.
What is Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
As we know that the value of m is directly varying with n, therefore, we can write the relationship as,
[tex]m \propto n[/tex]
Now, in order to remove the proportionality, we will add a constant,
[tex]m = kn[/tex]
As the value of m and n is given as 14 and 7, substitute the values in order to get the value of the constant k,
[tex]m = kn\\14 = k(7)\\\dfrac{14}{7} = k\\k=2[/tex]
We know the value of the constant k is 2, therefore, the equation can be written as,
[tex]m=2n[/tex]
Substitute the value of n as 16, to get the value of m,
[tex]m=2n\\m=2(16)\\m=32[/tex]
Hence, the value of m, when the value of n is 16 is 32.
Learn more about Expression:
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Q1
(b) Factorise
x2 – 36
(1 mark)
Answer:
(x+6)(x-6)
Step-by-step explanation:
Given: x²-36
Difference of Squares Formula: x²-a²=(x+a)(x-a)
Since 6²=36: x²-6²=(x+6)(x-6)
1.
A salesman earns $300 a week plus 20% of his sales. Which equation can be used to determine his
salary S if his weekly sales is x dollars?
Step-by-step explanation:
S = 300 x .20(x)
hope this helps
Simplify: 6^6/6^−3 Leave your answer in exponential form
Answer:
6⁹
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{6^6}{6^{-3}}[/tex]
Step 2: Simplify
Exponential Rule [Dividing]: [tex]\displaystyle 6^{6 - -3}[/tex]Rewrite: [tex]\displaystyle 6^{6 + 3}[/tex]Add: [tex]\displaystyle 6^{9}[/tex]Jamal's car travels an average of 16.7 miles per gallon of gas.
A full tank of gas is 20 gallons. Jamal has driven 292 miles
since he last filled his gas tank. How many more miles can
Jamal expect to travel on this same tank of gas?
Answer:
42 miles
Step-by-step explanation:
20 x 16.7 = 334 miles on a full tank of gas
he drove 292 miles so 334 - 292 = 42 miles left
What function represents the pattern shown in the table?
Given:
The table of values of an exponential function.
To find:
The function for the given table of values.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and b is growth factor.
From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.
[tex]9=ab^1[/tex] ...(ii)
[tex]36=ab^2[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{36}{9}=\dfrac{ab^2}{ab}[/tex]
[tex]4=b[/tex]
Putting [tex]b=4[/tex] in (ii), we get
[tex]9=a(4)^1[/tex]
[tex]\dfrac{9}{4}=a[/tex]
Putting [tex]a=\dfrac{9}{4},b=4[/tex] in (i), we get
[tex]y=\dfrac{9}{4}(4)^x[/tex]
[tex]y=9(4)^{x-1}[/tex]
The function notation with variable n is:
[tex]f(n)=9(4)^{n-1}[/tex]
Therefore, the correct option is D.
3. Brian paid $27 for 12 gallons of gasoline. To the nearest
cent, how much did 1 gallon of gasoline cost?
A. $0.44
B. $2.00
C. $2.25
D. $15.00
Answer:
C that was the answer to mine and it was right
Step-by-step explanation:
.Jorge has a square poster that measures 15 centimeters on a side. What is the perimeter of the poster in centimeters?
Answer:
[tex]A=225cm[/tex]
Step-by-step explanation:
From the question we are told that:
Sides of the square post
[tex]L=15cm[/tex]
Generally the equation for Area of a square A is mathematically given by
[tex]A=L*B[/tex]
Where L=B
Therefore
[tex]A=15*15[/tex]
[tex]A=225cm[/tex]
HELP PLEASE 10 POINTS AND BRAINLIEST
Answer:
the first (c) is the answer: ΔABC ≅ ΔPQR
Step-by-step explanation:
A laser beam moves along a straight line so that its velocity is given by v(t)=r²-4 feet/sec. What is the total distance, in feet, that the laser beam will have traveled between t=1 and t=3 seconds?
Answer:
4
Step-by-step explanation:
I used a calculator. I put integral values of 3 and 1 and then entered the equation inside absolute value bars
The total distance traveled by the laser beam in the given time interval is required.
The total distance traveled by the laser in the given time interval is 4 feet.
Equation of motionThe given equation is
[tex]v(t)=t^2-4[/tex]
The given time interval is from t = 1 to t = 3 seconds.
In order to find the distance traveled we need to integrate the equation with respect to time and between the given intervals.
[tex]0=t^2-4\\\Rightarrow t=\pm 2=+2[/tex]
The laser will change the direction at [tex]t=2[/tex]
[tex]\int_1^3 v(t)=\int_1^2t^2-4 dt+\int_2^3t^2-4 dt\\\Rightarrow \int_1^3 v(t)=\dfrac{t^3}{3}-4t|_1^2+\dfrac{t^3}{3}-4t|_2^3\\\Rightarrow \int_1^3 v(t)=\left|\dfrac{2^3}{3}-4\times 2-(\dfrac{1^3}{3}-4)+\dfrac{3^3}{3}\right|-\left|4\times 3-(\dfrac{2^3}{3}-4\times2)\right|\\\Rightarrow \int_1^3 v(t)=\dfrac{5}{3}+\dfrac{7}{3}\\\Rightarrow \int_1^3 v(t)=\dfrac{12}{3}\\\Rightarrow \int_1^3 v(t)=4\ \text{m}[/tex]
Since, here distance is asked the absolute value of each integral is used.
Learn more about equation of motion:
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Carlos buys a phone that cost $250. He pays a monthly rate of $75. What is the independent variable of this function ?
Answer: 250+75x
Step-by-step explanation: 250 is the flat charge on the phone, and he pays 75 dollars as a monthly rate. x represents the amount on months.
The diameter of a circle is 4cm. Find it area to nearewt tenth.
Answer:
12.6cm
Step-by-step explanation:
12.6 cm²
Area formula: (A = πr²)
If the diameter is 4 cm.. then that would mean the radius is 2 cm because the radius is half of the diameter. So, we already know the radius.. we just have to find the circumference.
Circumference formula: (C = πd) or (C = 2πr)
Finding the circumference : 3.14 × 4 = 12.56 cm
So, we now have the radius and circumference.
Radius = 2 cm
Circumference = 12.56 cm
Finding the Area : 3.14 × 2 × 2 = 12.56 cm²
So, 12.56 rounded to the nearest tenth is 12.6 cm².
Hope this helped! :)
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Answer:
¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.
Step-by-step explanation:
Si sacas una carta al azar de un mazo estándar de 52 cartas, ¿Cuál es la probabilidad de que obtengas una carta que sea menor a cinco o una de diamante?
A rocket gets launched straight up into space. What is a possible description
of the rate of change (slope)?
Answer:
sorry in a hurry
Step-by-step explanation:
A rocket gets launched straight up into space. What is a possible description
of the rate of change (slope)?
i need help please! will mark brainliest
Answer:
g= - 3x/x-2
Step-by-step explanation:
A suitcase is a rectangular prism whose dimensions are 1 1/4 feet by 1 1/2 feet by 2 1/4 feet. Find the volume of the suitcase. Tell me the answer as a mixed number in simplest form.
Use the formula: V= lwh
Good luck!
Answer:
V = 4.22ft^3
Step-by-step explanation:
Length: 2.25ft
Width: 1.5ft
Height: 1.25ft
Length x Width x Height = V
2.25 x 1.5 x 1.25 = 4.22ft, since we're dealing with volume of a 3D space, the answer is 4.22ft^3!
x^2-2x/x^2-y^2 - 2y-y^2/y^2-x^2
2−1⋅22−12−2−1⋅22−12
Step-by-step explanation:
Simón Plz help me giving brainliest
Answer:
Although this (attached) would be the correct answer always; A would be the most logical one since only one piece is shaded the opposite color.
Hope this Helps!:)
Thank you for the help
Please help out!!!! :///
Answer:
last option
Step-by-step explanation:
the middle term is the sum of 4k and 4k which is 8k
Please help! 3 questions ALL multiple choice if you answer them all you will get 30 points! I WILL GIVE YOU BRAINLIST! (NO LINKS PLEASE)
Answer:
I can help you on question 4, and the only 2 I saw was <ZAY and <WAZ. I hope I at least helped with that one.
Step-by-step explanation:
Please help me ASAP!!!
A circular pizza has a diameter of 16 inches. Each slice of pizza has a central of angle 45°. What is the area of each slice of pizza?
A. 3.1 in²
B. 6.13 in²
C.25.1 in²
D. 100.5 in²
Answer:
First, let's find the area of the whole pizza:
Area of circle = pi x r^2
r = 16 / 2
r = 8
Area of pizza = pi x 8^2 = 64pi
Now 45 degrees is 1/8 of the whole pizza (it is one-eighth of 360 degrees), and so a slice is proportional to the fraction of the area:
64pi / 8 = 8pi
The area of each slice is then 8pi in.^2
Step-by-step explanation:
Kamal makes $12.00 an hour at his job. Last week he earned $390. Write and solve an equation to determine how many hours Kamal worked last week. Enter the correct answers in the boxes.
Suppose you and a friend are playing a game that involves rolling a fair die. You roll the die and count how many times you must roll until you roll a 6. Which conditions for a binomial setting have been met for this scenario? Binary? Independent? Number of trials? Same probability?
Answer:
Binary-yes
Independent-yes
Number of trials- No
Same probability-yes
Step-by-step explanation:
Answer:
Binary?
✔ Yes
Independent?
✔ Yes
Number of trials?
✔ No
Same probability?
✔ Yes
Step-by-step explanation:
chris is a 150 pound 5 foot 10 inch 18 year old male and he requires 2,048 calories per day to maintain his weight when he doesn't exercise. When he plays basketball, he burns 231 additional calories per hour. Assuming he want s to maintain his current weight, how many more calories per day does he require if he plays basketball for four hours instead of two hours?
I NEED HEP ASAP I WILL GIBE BRAINLIEST ANSWER FOR WHOEVER ANSWERES FIRST
Answer:2
Step-by-step explanation:
URGENT!!!! BRAINLIEST FOR CORRECT ANSWER!
At the Little Rock Zoo, the cost for one children's ticket is $10 and the cost for one adult's ticket is $13. On Saturday, the zoo had a total of 1,465 people visit the zoo and took in a total of $16,603. How many CHILDREN visited the zoo? (Number Only)
Answer:
1663
Step-by-step explanation:
Three interior angles of a quadrilateral have measures of 100degree,120degree, and 80 degree. Find the fourth angle measure.
The fourth angle measure is..
Answer:
The fourth angle = 60°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral is 360°.
The fourth angle = 360° - 100° - 120° - 80° = 60°
Show that cos 30 degree + sin 60 degree / 1+ sin 30 degree + cos 60 degree is equal to cos 30 degree
Answer:
cos 30
Step-by-step explanation:
cos 30 + sin 60 / 1+ sin 30 + cos 60
= root3 / 2 + root3/2 / 1 + 1/2 + 1/2
= root 6/2 by 4/2
= root 6/4
= root 3/2
= cos 30
Answer:
cos 30
Step-by-step explanation:
Evaluate tan15°=tan(60°_45°)
Answer:
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
Decimal Form: