In order to determine the unit price of the pair of socks, you simply calculate the quotient between the cost of the package of the 4 pairs, between this number of pairs, just as follow:
35.16/4 = 8.79
Hence, the unit price of the pair of socks is $8.79
we need help solve the below multiple choice math question
Given:
216x and 180x
To find the greatest common factor:
Let us find the factors.
[tex]\begin{gathered} 216x=2\times2\times2\times3\times3\times3\times x \\ =2^3\times3^3\times x \\ 180x=2\times2\times3\times3\times5\times x \\ =2^2\times3^2\times x \end{gathered}[/tex]Thus, the greatest common factor is,
[tex]\begin{gathered} =2^2\times3^2\times x \\ =4\times9\times x \\ =36x \end{gathered}[/tex]Therefore, the correct option is E.
Use the distance formula to calculate the length of side AB
Given a line segment with two end points AB
Step 1: Write out the coordinates and define the (x,y) values
[tex]A(-2,2),x_1=-2,y_1=2[/tex][tex]B(3,2),x_2=3,y_2=2[/tex]Step 2: write out the formula for the distance between two point
[tex]|AB|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step 3: Substitute the x and y values in the above formula
[tex]\begin{gathered} |AB|=\sqrt[]{(3-(-2_{})^2+(2-2)^2} \\ =\sqrt[]{(3+2)^2-0^2} \\ =\sqrt[]{5^2} \\ =\sqrt[]{25} \\ =5\text{units} \end{gathered}[/tex]Hence the length of the side AB is 5 units
Given the two functions below with their provided domain, determine which function to substitute into and find the value of f(- 3) . Provide your numeric answer as well as a detailed response on how you determined your answer and why you believe correct. f(x) = 2x - 5 if x <= - 3 OR f(x) = - 3x + 4; x > - 3
f(x) = 2x - 5 is valid if x is less or equal to -3, while f(x) = -3x + 4 is valid only if x is greater than -3.
Therefore, we have: f(-3) = 2*(-3) - 5 = -6 - 5 = -11
………………………………………….………………….
Answer:
It is or D)Characteristic properties are afectted by the force of gravity
Greetings..
The matrices show the number of indoor and outdoor volunteers in different age groups. a)Create one matrix that shows the total number of indoor and outdoor volunteers in different age groups. Name the matrix T. Show your work.b)What is the value of the element at t_22 and what does that value indicate?c)Create a matrix by subtracting the men’s matrix from the women’s matrix. Name the matrix D. Show your work.d) What is the value of the element at d_21 and what does that value indicate?
To create a single matrix that shows the total number of outdoors ans indoors by age, we can add the two matrices:
[tex]T=\begin{bmatrix}{17} & 35{} \\ {}8 & 26{}\end{bmatrix}+\begin{bmatrix}{}9 & 20{} \\ {2}4 & 23{}\end{bmatrix}[/tex]Then we add:
[tex]T=\begin{bmatrix}{26} & {55} \\ {32} & {49}\end{bmatrix}[/tex]b) The value of:
[tex]T_{2,2}[/tex]Is the value of the second column in the secfond row. In this case, T_22 = 49
c) To substract the men's matrix from the women's matrix:
[tex]\begin{bmatrix}{9} & {20} \\ {24} & {23}\end{bmatrix}-\begin{bmatrix}{17} & {35} \\ {8} & {26}\end{bmatrix}=\begin{bmatrix}{-8} & {-15} \\ {16} & {-3}\end{bmatrix}=D[/tex]d) The value of
[tex]d_{2,1}=16[/tex]The first number is the row number, and the second number is the column number
Which point is located at (3, -1)?A.point AB.point DC.point ED.point F
B) point D
1) Examining that graph we can locate the point whose coordinates are (3,-1). Note that the x-coordinate is positive, and the y-coordinate is negative
2) This leads us to conclude that (3,-1) is in Quadrant IV and since the x-coordinate is 3 and the y-coordinate is 1 we can tell that
3) The answer is point D
Can you help me find the value of x? (Grade 10, angles)
Ok, so
Here we have a parallelogram:
Remember that the opposite angles are equal.
Now, the sum of all the internal angles of a parallelogram is 360°. This is:
[tex]\begin{gathered} 6x+9x+6x+9x=360 \\ 30x=360 \\ x=12 \end{gathered}[/tex]Therefore, x=12.
The value of your stock investment decreased by 42% after a stock market crash. What percentage increase in value would the stocks have to rise in oder to return to the value they were before the stock market crash? round your answer to the nearest tenth of a percent.
After the stock crash, we would have 100 - 42 = 58% of the initial amount.
To rise it in order to return to the amount before the crash, we would need a recovery rate r such as:
[tex]0.58\cdot(1+r)=1[/tex]Then we have:
[tex]\begin{gathered} 1+r=\frac{1}{0.58} \\ 1+r=1.724 \\ r=0.724=\text{ 72.4\%} \end{gathered}[/tex]What are the odds of selecting the correct answer on a multiple choice test when there are four answer choices?A. 1:4B. 1:3C. 1:5D. 1:2
Answer:
A. 1:4
Explanation:
The probability is defined as
probability = favorable outcome / total number of outcomes
Now in our case, the favorable outcome is selecting the correct answer choice.
Out of four answer choices, only one is correct.
Therefore, the probability that we select a correct answer is
[tex]1/4[/tex]Hence, choice A is the correct answer!
Hello could you please help me with this question? 7. Write a linear equation in slope-intercept form to model a tree 4 feet that grows 3 inches per year.
A linear equation in slope-intercept form is given by:
[tex]y=mx+b[/tex]Where:
b = starting height of tree = 4 feet = 48 inches
m = inches per year = 3 inches
x = the number of years of new growth
First, We convert the 4 feet in height to inches, to work in the same units. We know that 1 foot = 12 inches, therefore:
[tex]4(12)=48[/tex]48 is the starting height of tree in inches
Next, the equation is:
[tex]y=3x+48[/tex]2cm:500cm Simplified
Given:
2 cm: 500 cm.
Required:
To simplify the ratio.
Explanation:
Let us convert the given ratio in simplest form.
[tex]\begin{gathered} \frac{2}{500} \\ \Rightarrow\frac{1}{250} \\ \Rightarrow1:250 \end{gathered}[/tex]Thus, the simplified ratio is 1 cm : 250 cm.
Final Answer:
The simplified ratio is 1 cm : 250 cm.
Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. Hesets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections fothese graphs?noneonetwoinfinitely many
Given:
One side of the equation is a quadratic expression and the other side of the equation is linear.
sets the expressions equal to y and graphs the equations.
Required:
We need to find the greatest possible number of intersections of these graphs.
Explanation:
We know that the quadratic expression gives the parabola and the linea expression gives the line.
If the line crosses the parabola, then greatest possible number of intersections is two.
Final answer:
[tex]Two[/tex]Graph the following 5x+4y>20
SOLUTION
We want to graph
[tex]5x+4y>20[/tex]From the graph above, the shaded region is the required region.
Which exponential equation is equivalent to the logarithmic equation below?4 = ln xA.x = 10^4B.x = e^4C.x = 4eD.e = x4
Correct option: B
Calculate the distance between points (5,6) and (7,8)
Apply the distance formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where;
(x1,y1) = (5,6)
(x2,y2) = (7,8)
Replacing:
[tex]D=\sqrt[]{(7-5)^2+(8-6)^2}[/tex][tex]D=\sqrt[]{(2)^2+(2)^2}[/tex][tex]D=\sqrt[]{4+4}[/tex][tex]D=\sqrt[]{8}[/tex][tex]D=2.83[/tex]Find the equation of each of these lines. (Picture attached)
In order to ginde the line equation for each line, we need to choose two points in each part.
Case 1. Left line (purple)
In this case, we can choose the points
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,1) \end{gathered}[/tex]then the slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{1-0}=1[/tex]So, we have the following equation
[tex]y=mx+b\Rightarrow y=1\cdot x+b[/tex]where b is the y-intercept. We can find b by substituting in the last result one of the 2 given points. For instance, if we substitute point (0,0), we have
[tex]\begin{gathered} 0=1\cdot(0)+b \\ 0=0+b \\ \text{then} \\ b=0 \end{gathered}[/tex]Therefore, the line equation for the purple line is:
[tex]y=x[/tex]Case 2. Center line (red)
Similarly to the previous case, we need to choose two points along the line, for instance
[tex]\begin{gathered} (x_1,y_1)=(1,1) \\ (x_2,y_2)=(0,2) \end{gathered}[/tex]then, by applying the slope formula again, we have
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{0-1}=\frac{1}{-1}=-1[/tex]so, the red line has the form
[tex]y=-x+b[/tex]Again, we can find the y-intercept b by substituting one of the 2 given points. If we choose point (0,2), we get
[tex]\begin{gathered} 2=-(0)+b \\ 2=0+b \\ \text{then} \\ b=2 \end{gathered}[/tex]Therefore, the equation of the center line (red) is given by:
[tex]y=-x+2[/tex]Case 3. Blue line
Again, we need to choose 2 points along the line, for instance,
[tex]\begin{gathered} (x_1,y_1)=(3,-1) \\ (x_2,y_2)=(4,0) \end{gathered}[/tex]By substituting these point into the slope formula, we have
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-1)}{4-3}=\frac{1}{1}=1[/tex]So, the line has the form
[tex]y=1\cdot x+b[/tex]and by substituting the values of the point (4,0) into this equation, we have
[tex]\begin{gathered} 0=1\cdot4+b \\ 0=4+b \\ \text{then} \\ b=-4 \end{gathered}[/tex]So, the equation of the right line (blue) is given by:
[tex]y=x-4[/tex]If f(x) varies directly with x and f(x)= 70 when x=5 , find the value of f(x) when x=9.XRound you final answer to the nearest whole number.
Since f(x) varies directly with x, we can write
[tex]f(x)=k\cdot x[/tex]where k is the constant of proportionality. We know that when x=5, f(5)=70, then we have
[tex]70=k\cdot5[/tex]then, k is given as
[tex]\begin{gathered} k=\frac{70}{5} \\ k=14 \end{gathered}[/tex]Then, the equation which model the problem is
[tex]f(x)=14x[/tex]Now, we can substitute x=9 into this result. It yields,
[tex]\begin{gathered} f(9)=14(9) \\ f(9)=126 \end{gathered}[/tex]Therefore, the answer is 126
For the following vectors, find 5u - 2(v - W): u = <5, -1>, v = <-2, 1>, w = <-1, 0>0 <-7, 13><27, -7>0 <17, -10><13, 5>
Given:
[tex]\begin{gathered} u=(5,-1) \\ v=(-2,1) \\ w=(-1,0) \end{gathered}[/tex]To solve for 5u-2(v-w)
[tex]\begin{gathered} 5u-2(v-w) \\ 5(5,-1)-2((-2,1)-(-1,0)) \\ (25,-5)-2(-2--1,1-0) \\ (25,-5)-2(-2+1,1) \\ (25,-5)-2(-1,1) \\ (25,-5)-(-2,2) \\ (25--2,-5-2) \\ (25+2,-7) \\ (27,-7) \end{gathered}[/tex]-2.4(3x + 5) = 0.8(x + 3.5)
Given data:
The given expression is -2.4(3x+5)=0.8(x+3.5).
The given expression can be written as,
[tex]\begin{gathered} -2.4(3x+5)=0.8(x+3.5) \\ -7.2x-12=0.8x+2.8 \\ -8x=14.8 \\ x=-1.85 \end{gathered}[/tex]Thus, the value of x is -1.85.
find the values of x and yx= .........(simplify your answer)y=..........(simplify your answer)
we have that
Triangle ABC is an isosceles triangle
That neans
AB=BC
and
and BD is the perpendicular bisector of AC
therefore
AD=DC
y=2Find the value of x
we have that
In the triangle ABC
substitute
59+
The value of x is teh half of angle B
so
x=(1/2)(62)
x=31 degreesThe perimeter of a square must be greater than 122 inches but less than 134 inches. Find the range of possible side lengths that satisfy these conditions. Hint the perimeter of a square is given by p = 4s, where s represents the length of a side).
Let the perimiter of the square P
Statement 1
The perimeter of the square is greater than 122 inches
This can be expressed in inequality as
[tex]P>122[/tex]Statement 2
The perimeter of the square is less than 134 inches
This can be expressed in inequality as
[tex]P<134[/tex]Since P = 4S, hence
[tex]4s>122,4s<134[/tex]Solving for s gives
[tex]\begin{gathered} 4s>122 \\ \Rightarrow s>\frac{122}{4} \\ \Rightarrow s>30.5 \end{gathered}[/tex]Aslo
[tex]\begin{gathered} 4s<134 \\ \Rightarrow s<\frac{134}{4} \\ \Rightarrow s<33.5 \end{gathered}[/tex]Hence
[tex]s>30.5,s<33.5[/tex]Combining the inequalities gives
[tex]30.5[tex]\text{.}[/tex]5÷5=????????????????????
1) The division of 5 by 5 is equal to 1.
2) Any number divided per se is going to
A 5cm^3 holds 936 grains of rice. How many grains of rice would fit in one Dutchtown elementary school classroom with the dimensions 16cm x 12cm x 22 cm?
Explanation:
The question wants us to find the quantity of rice grain the classroom will hold when the dimension of the classroom is 16cm x 12cm x 22 cm
To resolve the question, we will first have to find the capacity of the new volume
[tex]\text{volume}=\text{length}\times breadth\times height=16\times12\times22=4224cm^3[/tex]So, we can now rephrase the question as:
If a 5 cm cube holds 936 grains of rice, how many grains of rice will a 4224 cm cube hold
To do so, we have
Making x, the subject by cross multiplying as shown above
We will have the answer to be:
[tex]790732.8\text{ grains of rice}[/tex]1) 8 + 3 x 2 - 4 Can You Explain On How To Do This Problem
10
Explanation:
Given expression: 8 + 3 x 2 - 4
To solve this we will apply the order of operations:
BODMAS (Bracket, Of, Division, Multiplication, Addition, and Subtraction) or PEDMAS (Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction) is used.
From the above, multiplication comes before addition and subtraction:
[tex]\begin{gathered} 8+3\times2-4=8\text{ + 6 -4 } \\ =\text{ 14 -4} \\ =\text{ 10} \end{gathered}[/tex]8 + 3 x 2 - 4 = 10
Find the X intercept of the equation 5x - 3y = 45
we have the linear equation
5x-3y=45
Find out the x-intercept (value of x when the value of y=0)
so
For y=0
substitute
5x-3(0)=45
5x=45
x=9
therefore
The x-intercept is the point (9,0)Solve the following system of linear equations using elimination. x-y=-3 5x+3y=1
S =(-1, 2)
1) Solving this system by Elimination Method, we have to first decide what term should be eliminated first
x-y=-3
5x+3y=1
2) Let's eliminate y, by multiplying the 1st equation by 3
x-y=-3 x 3
5x+3y=1
3x-3y=-9 Add both equations simultaneously
5x+3y=1
---------------------
8x = -8 Divide both sides by 8
x=-1
3) Plug x=-1 into the first equation
x-y=-3
-1 -y = -3
- y = -3 +1
-y = -2
y= 2
Hence, the solution for that system is (-1, 2)
The length of a rectangle is 3m4 and its width is 5m2. Find the area of the rectangle.15m68m68m215m2
Given:
length = 3m⁴
width = 5m²
The area of a rectangle is given by:
[tex]A=length\times width[/tex]hence:
[tex]A=3m^4\times5m^2=(3\times5)(m^{4+2})=15m^6[/tex]ANSWER
15m⁶
Which algebraic representation best describes the translation from RST to R'S'T
The general algebraic expression to represent a translation has the form:
(x+a, y+b)
Where the points are translated "a" points to the right and "b" points up.
From the given figure, we can see that the point "S" goes from (-6, -3) to (-2, 2)
Then, we can formulate the following expressions, to find "a" and "b":
x-coordinate of point S + a = x-coordinate of point S'
-6 + a = -2
-6 + 6 + a = -2 + 6
a = 4
y-coordinate of point S + b = y-coordinate of point S'
-3 + b = 2
-3 + 3 + b = 2 + 3
b = 5
Then, the algebraic expression that represents this translation is:
(x + 4, y + 5)
Then, the correct answer is the last option
Can a I have a tutor to help me with this ?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Interpret the given statements
[tex]\begin{gathered} height(h)=6ft \\ length(l)=2ft+width(w)=w+2 \\ width=w \end{gathered}[/tex]STEP 2: Write the formula for finding the volume of a rectangular prism
[tex]V=l\times w\times h[/tex]STEP 3: Substitute w+2 for length in the formula above
By substitution, this equation becomes;
[tex]\begin{gathered} l=w+2,h=6 \\ By\text{ substitution,} \\ V=(w+2)\times w\times6 \\ \mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac \\ 6w\left(w+2\right)=6w\cdot w+6w\times\:2 \\ =6ww+6w\times \:2 \\ =6w^2+12w \end{gathered}[/tex]Hence, the equation becomes:
[tex]\begin{equation*} 6w^2+12w \end{equation*}[/tex]Determine the y-interceptfor the following equation:7.2y + 4.5x = 72Y intercept:
The given expression is
[tex]7.2y+4.5x=72[/tex]To find the y-intercept, we have to solve the equation for y.
[tex]\begin{gathered} 7.2y=72-4.5x \\ y=\frac{72-4.5x}{7.2} \\ y=10-0.625x \end{gathered}[/tex]Remember that the y-intercept is the independent term.
Therefore, the y-intercept is 10, or the point (0, 10).