Please, don't close the session , the image its downloading
step 1
Assume that the value of m is positive
so
m-(-2)=3 1/2
m+2=3 1/2
m=3 1/2 -2
m=1 1/2
step 2
Assume that the vaue of m is negative
so
-2-(m)=3 1/2
-2-m=3 1/2
-m=3 1/2+2
m=-5 1/2
therefore
the possible values of m are1 1/2 and -5 1/2I need to check my answer with a tutor I got 700
Volume of triangular prism is given by the formula:
[tex]\begin{gathered} V=Area\text{ of cross-section }\times length \\ V=\frac{1}{2}\times base\times height\times length \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} V=\frac{1}{2}\times8\times7\times25 \\ V=\frac{1400}{2} \\ V=700\text{ cubic inches} \end{gathered}[/tex]Hence, the volume of the triangular prism is 700 cubic inches
Mais family drinks a total of 10 gallons of milk every 6 weeks. How many weeks does it take the family to consume 1 gallon of milk?
Given:
Mais family drinks a total of 10 gallons of milk every six weeks.
The proportion per week is,
[tex]\frac{10}{6}=\frac{5}{3}[/tex]The number of weeks required for a family to consume 1 gallon of the milk is,
[tex]\frac{6}{10}=\frac{3}{5}=0.6[/tex]Answer: the family will need 0.6 weeks to consume 1 gallon of milk.
OA Y A line has a slope of į and a y-intercept of (0,3). Which of the following represents the equation of the line? 1x - 3 1x + 3 • C. y = - 3x + + 1 / 1 • D. y = {(x - 3) B. 3 10
The first thing that we have to remember is the equation of a line in its slope-intercept form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
then we apply this formula to the conditions that are given to us
[tex]m=\frac{1}{2},b=3[/tex]then the answer is:
[tex]B\colon y=\frac{1}{2}x+3[/tex]determine if the following system is equations has no Solutions in family many solutions on exactly one solution X Plus y equals 5 2x minus y equals negative 3
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations
[tex]\begin{gathered} x+y=5(1) \\ 2x-y=-3(2) \end{gathered}[/tex]We solve by substitution
[tex]undefined[/tex]Find an equation of the tangent line at the indicated point on the graph of the function.w = g(z) = 1 + square root of (6 - z), (z, w) = (5, 2)w = - (1/2)z + (9/2)w = (1/2)z - (9/2)w = (1/2)z + (9/2)w = - (1/2)z - (9/2)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} w=g(z)=1+\sqrt{6-z} \\ (z,w)=(5,2) \end{gathered}[/tex]STEP 2: Explain Tangent line
Tangent Lines:
The tangent line to a function f(x) is a line that touches the graph of the function at one specific point of tangency where it has the same slope as the function at that point.
If x = a is the point of tangency, the tangent line can be written in slope-intercept form as:
[tex]\begin{gathered} y=mx+b \\ where\text{ }m=f^{\prime}(a)\text{ }and\text{ }y|_{x=a}=f(a) \end{gathered}[/tex]STEP 3: Find the tangent
We can first determine the slope of the tangent line by differentiating the function. Writing the function as:
[tex]g(z)=1+(6-z)^{\frac{1}{2}}[/tex]We find the derivative using the chain rule:
[tex]\begin{gathered} \mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g' \\ =\frac{d}{dz}\left(1\right)+\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right) \\ \frac{d}{dz}\left(1\right)=0,\frac{d}{dz}\left(\left(6-z\right)^{\frac{1}{2}}\right)=-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ \\ =0-\frac{1}{2\left(6-z\right)^{\frac{1}{2}}} \\ =-\frac{1}{2\left(-z+6\right)^{\frac{1}{2}}} \\ \\ =-\frac{1}{2}(6-z)^{-\frac{1}{2}} \end{gathered}[/tex]At the point of tangency, the slope is
[tex]\begin{gathered} g^{\prime}(5)=-\frac{1}{2}(6-5)^{-\frac{1}{2}} \\ g^{\prime}(5)=-\frac{1}{2} \end{gathered}[/tex]We can begin to write the equation of the tangent line in slope-intercept form
[tex]w=-\frac{1}{2}z+b[/tex]Substituting both coordinates of the point of tangency allows us to solve for the intercept:
[tex]\begin{gathered} 2=-\frac{1}{2}(5)+b \\ -\frac{1}{2}\left(5\right)+b=2 \\ -\frac{1}{2}\cdot \:5+b=2 \\ -\frac{5}{2}+b=2 \\ \frac{5}{2}+b+\frac{5}{2}=2+\frac{5}{2} \\ b=\frac{9}{2} \end{gathered}[/tex]The complete equation of the tangent line at (5,2) is then
[tex]w=-\frac{1}{2}z+(\frac{9}{2})[/tex]What are the equations for the asymptotes of this hyperbola? =1 64 = 55 O Av=1 V5. --VES 5 ty=-V55 5 x, y= 5 V 73 S O B.V=V73 -- = O c. v=zt, y=- OD 1 = 8, y = - 8 Too colon
The Solution:
Given the equation of the hyperbola below:
[tex]\frac{x^2}{9}-\frac{y^2}{64}=1[/tex]We are required to find the equation for the asymptotes of the above hyperbola.
By formula, the equation for the asymptotes is
[tex]\begin{gathered} y=\pm\frac{b}{a}x \\ \text{Where} \\ a^2=9 \\ a=\pm3 \\ b^2=64 \\ b=\pm8 \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} y=\pm\frac{8}{3}x \\ \text{This becomes} \\ y=+\frac{8}{3}x\text{ or }y=-_{}\frac{8}{3}x \end{gathered}[/tex]Therefore, the correct answer is option D.
Let cos(2x) - cos(x) = 0, where 0° sx s 180°. What are the possible values for x?O 60° onlyO 120° onlyO 0° or 120°O 60° or 180°
Given the equation:
[tex]\cos \mleft(2x\mright)-cos\mleft(x\mright)=0[/tex]First, we will express the cos (2x) in terms of cos (x) using the angle double rule:
[tex]\cos (2x)=2\cos ^2(x)-1[/tex]So, the given equation will be:
[tex]\begin{gathered} 2\cos ^2(x)-1-\cos (x)=0 \\ 2\cos ^2(x)-\cos (x)-1=0 \end{gathered}[/tex]The last equation has the form of the quadratic equation, so we will factor the equation:
[tex]\begin{gathered} (2\cos +1)(\cos x-1)=0 \\ 2\cos x+1=0\rightarrow\cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})=120\degree \\ \cos x-1=0\rightarrow\cos x=1\rightarrow x=\cos ^{-1}(1)=0\degree \end{gathered}[/tex]So, the answer will be option 3) x = 0° or 120°
X^2 - 25factor each expression completely
For the development of the exercise, we will need to remember some aspects of the factorization cases, specifically, the difference of squares. The first thing to do is to check if our algebraic expression complies with the rules to be able to apply this factorization case:
-Be a binomial
-Be separated by a minus sign.
-Each term must have an exact square root.
As it meets these criteria, we proceed to apply the factorization case as follows
[tex]\begin{gathered} (x-5)(x+5) \\ \text{ To prove the result:} \\ (x-5)(x+5)=x^2+5x-5x-25=x^2-25 \end{gathered}[/tex]Thus, the factorization for this expression is x^2-25= (x-5)(x+5).
A clinic purchased 8 dozen boxes of tissues. The total purchase cost was $198. How much did 12 boxes tissue cost?
Given,
The cost of 8 dozen boxes of tissue is $198.
As known that,
The are 12 boxes in one dozen.
[tex]8\text{dozen boxes=12}\times8\text{ =96 boxes}[/tex]There are total 196 boxes of cost $198.
The cost of 12 boxes of tissue is,
[tex]\cos t\text{ of 12 box =}\frac{198}{96}\times12=24.75[/tex]Hence, the cost of 12 boxes is $24.75.
A of values of a linear function is shown below.
The slope of a linear function is given by the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where m is the slope, (x1,y1) and (x2,y2) are two points on the line. We can find these values in the given table.
By replacing (-1,-2) and (0,-3) we can find the slope:
[tex]m=\frac{-3-(-2)}{0-(-1)}=\frac{-3+2}{0+1}=-\frac{1}{1}=-1[/tex]The slope is -1.
The y-intercept is the y-value at x=0.
In the table we can see when x=0, y=-3
The y-intercept is -3.
The slope-intercept equation of a line is given by:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. If we substitute these values we have:
[tex]\begin{gathered} y=-1x-3 \\ \\ equation \\ y=-x-3 \end{gathered}[/tex]Match the equation to the correct graph.1. () --2x + 32. f(x) = 2x + 33. f(x) = -3x14. (X) = 3x - 1ABC СD
Let us match the equations with the positive slopes with their corresponding graphs, so the positive slope equations are.
[tex](2)\rightarrow f(x)\text{ =2x+3 and (4)}\rightarrow\text{ f(x) = 3x-1}[/tex]Here, if we look a bit close, we can see that one has a y-intercept of 3 and another has y-intercept of -1 so form the graph
(2) matches with (A) and (4) matches with (B)
Now let us move on to the equations that have negative slope.
[tex](1)\text{ }\rightarrow f(x)-2x+3\text{ (3)}\rightarrow f(x)\text{ -3x -1}[/tex]Similarly these two have negative slopes, so they must be of C and D graphs.
(1) has a positive 3 y-intercept, therefore, it matches with graph (D) and (3) has a negative 1 y-intercept therefore it matches with option (C) or graph.
Solve the compound inequality and give your answer in interval notation.82 +4 > 20 OR — 62 +3 >- 3
Problem
We have the following inequality given:
8x +4 > 20
OR
-6x+3 >= -3
Solution
For this case we can start with the first inequality and we got:
We can subtract 4 in both sides
8x > 20-4
8x >16
And now we can divide both sides by 8
x > 2
-6x +3 >= -3
If we subtract 3 in both sides we got:
-6x >= -6
And dividing by -6 in both sides we got:
x <1
So then on interval notation we got:
[tex](-\infty,1)U(2,\infty)[/tex]Hi I need help with this question, please and thank you
ANSWER
Factoring Pattern: C. difference of Cubes
Factored Form: (x - y)(x^2 +xy + y^2)
EXPLANATION
Step 1:
If you observe the expression very well, both terms are Perfect Cubes;
Hence, Difference of Cubes formula would be applied to factorize the expression.
Step 2:
Difference of Cubes formula
[tex](a-b)(a^2+ab+b^2)[/tex]where a = x and b = y.
Step 3:
Rewriting the Expression
[tex]\begin{gathered} (x-y)(x^2+xy+y^2) \\ =x^3+x^2y+xy^2-x^2y-xy^2-y^3) \\ \text{ = x}^3-y^3 \end{gathered}[/tex]Hence, the Factored Form is (x - y)(x^2 +xy + y^2)
Solve the system by elimination. 2x+3y=06x+9y=8
Given:
The system of equations is,
2x+3y=0
6x+9y=8
Explanation:
Multiply the equation 2x+3y=0 by 3 and subtract from equation 6x+9y=8
.
[tex]\begin{gathered} 6x+9y-3(2x+3y)=8-3\cdot0 \\ 6x+9y-6x-9y=8-0 \\ 0=8 \end{gathered}[/tex]Since no variable left and left-hand side and right-hand side of the equation are unequal. So lines are parallel lines and there is no solution.
Answer: No solution
Find the surface area and the volume of the figure shown. Note that the figure may not be drawn to scale.7d2 yd9 ydThe surface area of the figure isM (Simplify your answer.)The volume of the figure isV (Simplify your answer.)
In order to find the surface area we need to calculate the area of each face
We have two faces with his shape
[tex]A_1=(2\cdot9)+(3\cdot2)=24yd^2[/tex]then we have rectangles in the other faces the formula of the area of a rectangle is l times w where l is the length and w is the width
where A2 is the bottom face and A7 is the lateral face that we can't see in the image but we know they exist
[tex]A_2=9\cdot12=108yd^2[/tex][tex]A_3=12\cdot2=24yd^2[/tex][tex]A_4=7\cdot12=84yd^2[/tex][tex]A_5=3\cdot12=36yd^2[/tex][tex]A_6=2\cdot12=24yd^2[/tex][tex]A_7=5\cdot12=60yd^2_{}[/tex]In order to calculate the surface area we sum all the areas we found remember we have 2 faces with the A1
[tex]\begin{gathered} SA=2A_1+A_2+A_3+A_4+A_5+A_6+A_7_{} \\ \end{gathered}[/tex]we substitute the values
[tex]SA=2(24)+108+24+84+3624+60=384yd^2[/tex]The surface area of the figure is 384 yd^2
Then for the volume, we have the next formula
[tex]V=A_1\cdot w[/tex]where
A1=24yd^2
w=12yd
we substitute the values
[tex]V=24\cdot12=288yd^3[/tex]the volume of the figure is 288yd^3
Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
One advantage of the English system is that units are based on powers of 10.
Question content area bottom
Part 1
Choose the correct answer below.
A.
The statement is true because 1 foot in the English system is about 10 times longer than 1 inch.
B.
The statement is false. It should be changed to one advantage of the English system is that to change units within the English system, successively smaller units involve division by 10 and successively larger units involve multiplication by 10.
C.
The statement is false. It should be changed to one advantage of the English system is that units are based on parts of the body.
D.
The statement is false. It should be changed to one advantage of the metric system is that units are based on powers of 10.
The statement that one advantage of the English system is that units are based on powers of 10 is D. The statement is false. It should be changed to one advantage of the metric system is that units are based on powers of 10.
What is a metric system?Our base ten number system is used by the metric system of measurement. The metric system has an advantage over the US system in that it is possible to convert from one unit of measure to another simply by multiplying or dividing the supplied number by a power of ten.
The metric system is built on powers of ten, which is convenient because: A measurement represented by a rational number in the metric system remains a rational number after metric unit conversion. (For instance, 250 mm = 25 cm =.25 m.)
Because all metric units are based on multiples of 10, conversions are fairly straightforward. The metric system was first used in France in 1795. The International System of Units is a metric-based measurement system.
In conclusion, the correct option is D.
Learn more about metric system on:
https://brainly.com/question/1837503
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A video rental store charges a $20 membership fee and $2.50 for each video rented.1) Write and graph a linear equation (y=mx+b) to model this situation.2) If 15 videos are rented, what is the revenue?3) If a new member paid the store $67.50 in the last 3 months, how many videos were rented?
Given that the membership fee of $20 is constant, the amount of video rented is $2.50 per video.
It can be observed that the independent variable is the number of video rented at the rate of $2.50, which can also be regarded as the gradient. The membership fee is constant, while the revenue is the dependent variable that is determine based on varied number of video rented.
This information can modelled using the linear equation below
[tex]\begin{gathered} y=mx+b \\ m=2.5 \\ b=20 \\ y=\text{revenue} \\ x=number\text{ of video rented} \\ \text{The modelled equation would be} \\ y=2.5x+20 \end{gathered}[/tex]The graph of the modelled linear equation is as shown below
Hence, the linear equaton modelled is y = 2.5x + 20 and the graph is as shown above
2) If 5 videos are rented, the revenue is as calculated below:
[tex]\begin{gathered} y=2.5x+20 \\ x=15 \\ y=2.5(15)+20 \\ y=37.5+20 \\ y=57.5 \end{gathered}[/tex]Hence, the revenue when 15 videos were rented is $57.50
3) If a new member paid the store $67.50 in the last 3 months, the number of video rented would be
[tex]\begin{gathered} y=2.5x+20 \\ y=67.50 \\ 67.50=2.5x+20 \\ 67.50-20=2.5x \\ 47.50=2.5x \\ \text{LHS}=\text{RHS} \\ 2.5x=47.50 \end{gathered}[/tex][tex]\begin{gathered} \frac{2.5x}{2.5}=\frac{47.50}{2.5} \\ x=19 \end{gathered}[/tex]Hence, the number of videos rented when a new member paid $67.50 is 19
The figure shows a Square and 4 congruent isosceles triangles the lenght of leg x is 12 feet,What is the lenght in feet of the hypnotese of each triangle?
In order to find the hypotenuse of each triangle we are going to focus on the sides of one of them:
Since the figure in the center is a square then all its sides lenght is 10 feet:
Since the triangle is divided in halfs, then:
Now we can find its hypotenuse. We have the following triangle:
We know, by the Pythagoras Theorem, that:
[tex]\begin{gathered} x^2+y^2=hypotenuse^2 \\ \downarrow \\ 12^2+5^2=hypotenuse^2 \\ \downarrow \\ 144^{}+25^{}=hypotenuse^2 \\ 169=hypotenuse^2 \end{gathered}[/tex]Since,
13² = 169
then
13² = hypotenuse²
Then
13 = hypotenuse
Answer- the hypotenuse of each triangle is 13ftdetermine the distance between the hikers to the nearest tenth of a mile
Solution
For this case we can use the Pythagoras theorem and we can do this:
[tex]c=\sqrt[]{3^2+2.5^2}=3.905[/tex]And if we round we got:
3.9 mi
From the diagram below, what is the measure of the angle of elevation from point B?
The answer is 39°, because the angle A from the slope to the upper horizontal line is the same as the angle B to the lower horizontal line.
HUHS is looking to buy more sports equipment for the upcoming school year. The function C(x) = 314 - 7.7x models the cost of shipping the equipment, x, to the school. The function R(x) = 19.3x models the revenue the school earns from fundraising for the equipment, x, they want to buy. Which function, P9x), models the profit that the school earns if they fundraise for the equipment? (Profit = Revenue - Cost)
According to the information the function for the profit p(x) is obtained by substracting the revenue and the costs.
[tex]p(x)=R(x)-C(x)[/tex]replace the functions into the equation
[tex]p(x)=19.3x-(314-7.7x)[/tex]distribute the negative sign
[tex]p(x)=19.3x-314+7.7x[/tex]simplify the equation
[tex]p(x)=27x-314[/tex]The pie chart below shows the average words per minute someone can type. If the total number of people surveyed is 10000, approximately how many of them type 45 words per minute or less?
According to the Pie Chart, the number of people who type 45 words per minute or less, covers approximately half of the chart. Hence:
People type 45 words per minute or less ≈ 45%.
45% of 10000 = 4500
ANSWER
4500
Farmer buys a tractor for 159,000 and assumes the trade in value of 87,000 after 10 years . The farmer uses a constant rate of depreciation to determine the annual value of the tractor . Find the linear model
Hello there. To solve this question, we have to find the linear model of the annual value of the tractor.
In this case, we want to find a line equation as follows:
[tex]y=mt+b[/tex]Where m is the slope of the line, b is the y-intercept and t is the time in year.
We know the farmer bought a tractor for $159.000 and assumes the trade in value of $87.000 after 10 years.
Think of these values as points in a graph: (0, 159000) and (10, 87000)
Since the graph of this function is on the ty plane, we can use the slope formula to find the value of m:
[tex]m=\frac{87000-159000}{10-0}=-\frac{72000}{10}=-7200[/tex]Now, plugging in the value of m and any of the points in the equation of the line, we calculate the value of b:
[tex]\begin{gathered} 159000=-7200\cdot0+b \\ b=159000 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-7200t+159000[/tex]B) What is the depreciated value of the tractor after 6 years?
Plugging in t = 6, we get:
[tex]y=-7200\cdot6+159000=115800[/tex]C) When will the depreciated value fall below $80.000?
In this case, we solve for the inequality:
[tex]\begin{gathered} y<80000 \\ -7200t+159000<80000 \end{gathered}[/tex]Subtract 159000 on both sides of the inequality
[tex]-7200t<-79000[/tex]Divide both sides of the inequality by a factor of -7200. Remember this flips the inequality sign.
[tex]t>10.97\text{ years}[/tex]Since we need to round to the nearest integer:
The depreciated value will fall below $80.000 on the 11th year.
The graph will look like the following:
Out of scale. The correct option is indeed C.
please help me to do this problem please. Quadratic Formula
Applying the quadractic formula:
[tex]m=\frac{5\pm\sqrt[]{25-(4)(1)(-14)}}{2}=\frac{5\pm9}{2}[/tex]then the solutions will be m=7 and m=-2What is the equation written in point slope form given (2,5) and (5,9)? y-y1=m(x-x1) (fill in the blanks y- = (x-)
(2,5) ==> x1 = 2, y1 = 5
(5,9) ==> x2 = 5, y2 = 9
slope m = (y2 - y1)/(x2 - x1) = (9 - 5)/(5 - 2) = 4/3
The slope form equation is:
y - y1 = m(x - 1)
If we use the values for this exercise:
y - 5 = (4/3)(x - 2)
Answer:
y - 5 = (4/3)(x - 2)
expand the following expresion 8 (3x + 10y)
Expand the expression.
[tex]\begin{gathered} 8(3x+10y)=8\cdot3x+8\cdot10y \\ =24x+80y \end{gathered}[/tex]Thus expression after expand is 24x + 80y.
Find the equation of the line described. Write the equation in slope intercept form. Graph the line. Vertical line that contains (3,4)What is the equation of the line?
The given cordinate is (3, 4)
x = 3
y = 4
Since it is a vertical line, it would pass through x = 3
Thus, the equation of the line is
x = 3
The graph is shown below
if f(x)=-5x+2 g(x)=2x-7 find (f/g) (x)
To solve this answer, we just have to divide the functions
[tex](\frac{f}{g})(x)=\frac{-5x+2}{2x-7}[/tex]Hence, the resulting function is[tex](\frac{f}{g})(x)=\frac{-5x+2}{2x-7}[/tex]For each equation, choose the statement that describes its solutiorIf applicable, give the solution.
Part A.
The equation is given by
[tex]4(x+1)+x=3(x-2)+2[/tex]By distributing the number form into the parenthesis on the left hand side and the number 3 into the parenthesis of the right hand side, we have
[tex]4x+4+x=3x-6+2[/tex]By combinig similar terms, we get
[tex]5x+4=3x-4[/tex]Then, by subtracting 3x to both sides, we have
[tex]2x+4=-4[/tex]and by subtracting 4 to both sides, we get
[tex]2x=-8[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]Then, the solution for part A is x=-4.
Part B
In this case, the equatiion is
[tex]5(2+v)-v=10+4(v+1)[/tex]Then, by distributing the number 5 into the parenthesis and the number 4 into the parenthesis on the right hand side, we have
[tex]10+5v-v=10+4v+4[/tex]By combining similar terms, we have
[tex]10+4v=14+4v[/tex]and by subtracting 4v to both side, we have
[tex]10=14[/tex]which is an absurd result. Therefore, the answer for part B is. No solution
Angelique is buying towels for her apartment. She finds some green towels, x, that cost $7 each and blue towels, y, that cost $9 each. She wants to buy at least 5 towels, but does not want to spend more than $60. How many of each towel can she purchase? Enter the system of inequalities that represents the situation. Then select the graph of the system and Select one possible solution.
Explanation:
x is the number of green towels and y is the number of blue towers.
If she wants to buy at least 5 towels, the inequality that represents the situation is:
x + y ≥ 5
On the other hand, she doesn't want to spend more than $60, so
7x + 9y ≤ 60
Because 7x is the total cost of the green towels and 9y is the total cost of the blue towels.
Now, the graph that represents the system of inequalities is graph A. because the red region is the region above the line x + y = 5 and the second region is the region below the line 7x + 9y = 60.
Finally, we need to select a point that belongs to the purple region. So, Angelique could buy 3 and 4 green and blue towels respectively.
Answer:
The system of inequalities is x + y ≥ 5 and 7x + 9y ≤ 60
Graph A
Angelique could buy 3 and 4 green and blue towels respectively.