Given:
The initial number of MNMs I have, x=200.
The number of MNM's eat by me every minute, p=15.
The initial number of MNMs my friend have, y=300.
The number of MNM's eat by friend every minute, q=25.
Let n be the number of minutes after which both will have the same number of MNM. Then, the amount of MNM remaining with me after n minutes is,
[tex]x-pn[/tex]The amount of MNM remaining with my friend after n minutes is,
[tex]y-qn[/tex]Equate the above expressions and substitute the values to find the number of minutes n.
[tex]\begin{gathered} x-pn=y-qn \\ 200-15n=300-25n \\ 25n-15n=300-200 \\ 10n=100 \\ n=\frac{100}{10} \\ n=10 \end{gathered}[/tex]Therefore, I will have the same number as my friend after 10 minutes.
The number of minutes taken by me to finish 200 MNM's is,
[tex]\begin{gathered} m=\frac{x}{p} \\ =\frac{200}{15} \\ =13\frac{5}{15} \\ =13\frac{1}{3}\text{minutes} \\ =13\text{minute}+\frac{1}{3}\min utes\times\frac{60\text{ seconds}}{1\text{ minute}} \\ =13\text{ minutes +20 seconds} \end{gathered}[/tex]So, I will take 13 minutes 20 seconds to finish the MNM's.
The number of minutes taken by my friend to finish 300 MNM's is,
[tex]\begin{gathered} k=\frac{y}{q} \\ =\frac{300}{25} \\ =12\text{ minutes} \end{gathered}[/tex]So, the friend will take 12 minutes to finish the MNM's.
So, I will finish
Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
2-x+ 3-X-4
where a and b are integers.
Work out the value of a and the value of b.
can be written as a single fraction in the form
ax+b
x²-16
Answer:
2-×+3-×-4=0
Step-by-step explanation:
×=1\2
0.5,2`1
Evaluate 2(x - 4) + 3x - x^2 for x = 2.O A. -6O B. -2O C. 6O D. 2
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week.
The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,
W = W(n) = Pb'
Here P = 106 and b = 1.04
Hence the required formula is,
⇒ W = 106 × 1.04ⁿ
Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
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The question seems to be incomplete the correct question would be
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.
If y = (x/x+1)5, then dy/dx
The value of dy/dx is 5x^4 / (x + 1)^6.
What is the derivative?
A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable.
The given function is y = (x / (x + 1))^5
Taking derivative on both sides,
dy/dx = d/dx (x / (x + 1))^5)
Using chain rule,
dy/dx = 5(x / x + 1)^4 x d/dx (x / x + 1)
Using the quotient rule of derivative,
d/dx (x / x + 1) = 1 / (x + 1)^2
So,
dy/dx = 5(x / x+1)^4 x (1 / (x + 1)^2)
dy/dx = 5x^4 / (x + 1)^6
Therefore, the derivative of the given function is, dy/dx = 5x^4 / (x + 1)^6.
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Ms. Kirk has at most $75 to spend on workout supplements. She boughtthree containers of protein powder for $47. She wants to buy protein barsthat cost $4 each. How many protein bars can she buy?
total money is 75$
protein cost = 47$
so the remaining money is
75 - 47 = 28 $
now she bought the protein bars of 28$
cost of one protein bar is 4$
so the number of protein bars that she bought is
[tex]=\frac{28}{4}=7[/tex]so she bought 7 protein bars.
find 2x:3y if x:y = 2:5
4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex]Which tool would be best to solve this problem?Pythagorean TheoremTriangle Angle Sum TheoremTangent RatioSine RatioCosine RatioUse that tool to solve for x. Show all work on the sketchpad or on your paper.
To get the value of x,
We use triangle sum theorem:
Triangle Sum Theorem:
The sum of all angles in a triangle is equal to 180 degrees.
In the triangle
We have 90 degree, 22 degree and one x
So,
x + 90 + 22 =180
x + 112 = 180
x = 180-112
x = 68 degree
Answer: x = 68
1. Alice made the conjecture below.(a + b)2 = a + b2OWhich values of a and b are not counterexamples to the conjecture?a = 1, b = 1a = 0, b = 1aa = -1, b = 1a = -1, b = 2
the expression is
(a+b)^2=a+b^2
substitute a=1 and b=1
(1+1)^2 = 1+1^2
4=2
that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.
now substitute a=0, b=1
(0+1)^2 = 0+1^2
1=1
so this is true for the above expression.
now for a=-1, b=1
(-1+1)^2 = -1+1^2
0=0
this is true.
now for a=-1, b=2
(-1+2)^2 = -1+2^2
1=3
that is not possible
so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.
The next algebra test is worth 100 points and contains 35 problems. Multiple-Choice questions are worth 2 points each and word problems are 7 points each. How many of each type equation are there?
Let
x ----->number of multiple-choice questions
y ----> number of word problems
so
we have
x+y=35 --------> equation 1
2x+7y=100 -----> equation 2
solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
therefore
x=29
y=6
number of multiple-choice questions is 29
number of word problems is 6
What does the slower car travel at Then what does the faster car travel at
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
Find the value of 4v-8 given that 11v-8 = 3.Simplify your answer as much as possible.
Given that 11v - 8 = 3
add 8 to both sides
11v = 3 + 8
11v = 11
Divide both sides by 11
v = 1
to simplify 4v - 8
= 4 (1) - 8
= 4 - 8
= -4
Find the length of AB given that DB is a median of the triangle AC is 46
ANSWER:
The value of AB is 23
STEP-BY-STEP EXPLANATION:
We know that AB is part of AC, and that DB cuts into two equal parts (half) since it is a median, therefore the value of AB would be
[tex]\begin{gathered} AB=\frac{AC}{2} \\ AB=\frac{46}{2} \\ AB=23 \end{gathered}[/tex]I need help with a math question. I linked it below
1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:
[tex]\begin{gathered} \frac{b}{55}+8>6 \\ \frac{b}{55}>-8+6 \\ \frac{b}{55}>-2 \\ 55\cdot\frac{b}{55}>-2\cdot55 \\ b>-110 \end{gathered}[/tex]Note that we could do it in two steps. Subtracting and then multiplying and dividing
What's the equation of the axis of symmetry of g(x)=x^{2}+4 x+3?A) x=0B) x=-2C) x=2D) x=3
Given a quadratic equation of the form:
[tex]f(x)=ax^2+bx+c[/tex]The equation of the axis of symmetry is obtained using the formula:
[tex]x=-\frac{b}{2a}[/tex]From the given quadratic equation:
[tex]\begin{gathered} g\mleft(x\mright)=x^2+4x+3 \\ a=1 \\ b=4 \end{gathered}[/tex]Therefore, the equation of the axis of symmetry of g(x) is:
[tex]\begin{gathered} x=-\frac{4}{2\times1} \\ x=-2 \end{gathered}[/tex]The correct option is B.
Review: Solve for Area AND Circumference. A giant holiday cookie has a radius of 5 inches. What is the area of the cookie? What is the circumference of the cookie?
Remember that the formual for the area of a circle is:
[tex]A=\pi r^2[/tex]And the formula for the circumference is:
[tex]C=2\pi r[/tex]Using this formulas and the data given,
[tex]\begin{gathered} A=\pi(5^2)\Rightarrow A=78.54 \\ C=2\pi(5)\Rightarrow A=31.42 \end{gathered}[/tex]The cookie has an area of 78.54 square inches and a circumference of 31.42 inches
In the diagram below, BS and ER intersect as show. Determine the measure of
Which best represents the number of square centimeters in a square foot?A 366 square centimeters B 144 square centimeters C 930 square centimeters D 61 square centimeters
Answer:
C. 930 square centimeters
Explanation:
First, recall the standard conversion between cm and ft.
[tex]1\text{ ft}=30.48\operatorname{cm}[/tex]Therefore:
[tex]\begin{gathered} (1\times1)ft^2=(30.48\times30.48)cm^2 \\ =929.03\operatorname{cm}^2 \\ \approx930\text{ square cm} \end{gathered}[/tex]The correct choice is C.
what is the area if one of the triangular side of the figure?
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
Identify the following forms of factoring with the correct method of solving
Given:
There are given the equation:
[tex]90x^3-20x[/tex]Explanation:
To find the factor of the given equation, first, we need to take a common variable from the given equation:
[tex]90x^3-20x=x(90x^2-20)[/tex]Then,
[tex]\begin{gathered} 90x^3-20x=x(90x^2-20) \\ =10x(9x^2-2) \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex]\begin{equation*} 10x(9x^2-2) \end{equation*}[/tex]A seamstress has three colours of ribbon; the red is 126cm, the blue is 196cm and the green
is 378cm long. She wants to cut them up so they are all the same length, with no ribbon
wasted. What is the greatest length, in cm, that she can make the ribbons?
Answer:
14cm is the greatest length
Step-by-step explanation:
Hi!
So the question is basically asking for the greatest common factor between each of these numbers (if I understood the question right so here we go) :
The GCF in this case is 14:
126 / 14 = 9
196 / 14 = 14
378 / 14 = 27
Please feel free to ask me any more questions that you may have!
and Have a great day! :)
Solve the following simultaneous equation using the inverse matrix method
3x + 4y = 18
4x - y = 5
The values of x and y obtained by inverse matrix method are 2 and 3 respectively
What is an inverse matrix?An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.
The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;
A·X = B
The system of equations is presented as follows;
3·x + 4·y = 18
4·x - y = 5
From the above system of equations, we have:
[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]
[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]
[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]
From the equation, A·X = B, we have;
[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]
Where: A⁻¹ is the inverse matrix of A, which is found as follows;
[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]
[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]
Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;
[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]
[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]
The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;
[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
Therefore;
x = 2 and y = 3
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Select the correct answer from the drop-down menu.Find the polynomial,{4'" is the solution set of
Let P(x) be the polynomial such that the given set is its solution set.
Now notice that:
[tex]\begin{gathered} x=-\frac{1}{3}\Rightarrow x+\frac{1}{3}=0\Rightarrow3x+1=0, \\ x=4\Rightarrow x-4=0. \end{gathered}[/tex]Therefore (x-4) and (3x+1) divide to P(x), then:
[tex]\begin{gathered} Exists\text{ k such that:} \\ P(x)=k(x-4)(3x+1). \end{gathered}[/tex]Simplifying the above result we get:
[tex]P(x)=k(3x^2-11x-4).[/tex]Setting k=1 we get that:
[tex]P(x)=3x^2-11x-4.[/tex]Answer: Second option.
In a probability experiment, Craig rolled a six-sided die 62 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
Answer:
31/55
Step-by-step explanation:
Write a quadratic equationwith vertex (3,-6) and otherpoint (-7,14). Solve for a!
We have to find the parameter a of a quadratic equation knowing the following
• The vertex is (3,-6).
,• A random point is (-7,14).
Based on the given information, we have the following
[tex]\begin{gathered} h=3 \\ k=-6 \\ x=-7 \\ y=14 \end{gathered}[/tex]The vertex form of a quadratic equation is
[tex]y=a(x-h)^2+k[/tex]Replacing all the givens, we have
[tex]14=a(-7-3)^2-6[/tex]Now, we solve for a
[tex]\begin{gathered} 14=a(-10)^2-6 \\ 14=a(100)-6 \\ 14+6=100a \\ 100a=20 \\ a=\frac{20}{100}=\frac{1}{5} \end{gathered}[/tex]Therefore, a is equal to 1/5.Write the equation of the line when the slope is 1/5 and the y-intercept is 13.
Given:
• Slope, m = 1/5
,• y-intercept = 13
Let's write the equation of the line.
To write the equation of the line, apply the slope-intercept equation of a line:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept.
Thus, we have:
m = 1/5
b = 13
Plug in the values in the equation:
[tex]y=\frac{1}{5}x+13[/tex]Therefore, the equation of the line is:
[tex]y=\frac{1}{5}x+13[/tex](4xy³y⁴)(5x²y) expand and simplify
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(4xy³y⁴)(5x²y)
Step 02:
[tex](4xy^3y^4)(5x^2y)=(4xy^7)(5x^2y)=20x^3y^8^{}[/tex]This is the solution.
[tex]20x^3y^8^{}[/tex]Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.
The distance between 2 points (x1, y1) and (x2, y2) is calculated as:
[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:
[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]Answer: the distance is 15
Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)
Step 1
Given the triangle, ABC translated to A'B'C'
Required to find the algebraic description that maps triangle ABC and A'B'C'
Step 2
The coordinates of points A, B,C are in the form ( x,y)
Hence
[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]Step 3
Find the algebraic description that maps triangle ABS TO A'B'C'
[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]The algebraic description is found using the following;
[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]Hence the answer is option B
ZA and ZB are supplementary angles. If mZA= (8x – 27) and m ZB = (4x + 3), then find the measure of ZA.
Supplementary angles sum up to 180 degrees.
Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find
Supplementary angles sum up to 180 degrees.
Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find
