Given the equation:
[tex]y+5x=7[/tex]we can find its slope if we write it in the y=mx+b form:
[tex]\begin{gathered} y+5x=7 \\ \Rightarrow y=-5x+7 \end{gathered}[/tex]Now, we know as a general rule, that the slope of the perpendicular of the line that has slope m, is -1/m, more clearly:
[tex]\begin{gathered} \text{if m is the slope of the line} \\ \Rightarrow m_p=-\frac{1}{m}\text{ is the slope of the perpendicular line} \end{gathered}[/tex]So, in this case we have:
[tex]\begin{gathered} m=-5 \\ \Rightarrow m_p=-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5} \\ m_p=\frac{1}{5} \end{gathered}[/tex]now we use the slope-point formula to find the equation of the perpendicular line:
[tex]\begin{gathered} (x_0,y_0)=(10,-4) \\ m_p=\frac{1}{5}_{} \\ y-y_0=m(x-x_0)_{} \\ \Rightarrow y-(-4)=\frac{1}{5}(x-10) \\ \Rightarrow y+4=\frac{1}{5}x-\frac{10}{5} \\ \Rightarrow y=\frac{1}{5}x-2-4=\frac{1}{5}x-6 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]therefore, the line perpendicular to y+5x=7 that passes through (10,-4) is y=1/5x-6
You roll a six-sided die. What is the probability that it is an odd number or greater than three? Round your answer to the nearest thousandth. The probability is about
the total possible outcome of a die is 6
n(T) = 6
the sample space {1,2,3,4,5,6}
the odd numbers are {1,3,5}
thus n(O) = 3
numbers greater than 3 are {4,5,6}
thus n(>3) = 3
the probability of getting an odd number or a number greater than 3
is Pr(O) U Pr(>3)
[tex]\begin{gathered} Pr\text{ (O) = }\frac{n(O)}{n(T)}=\frac{3}{6}=\frac{1}{2} \\ Pr(>3)\text{ = }\frac{n(>3)}{n(T)}=\text{ }\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} Pr\text{ (O U >3) = Pr(O) + Pr(>3)} \\ \text{ = }\frac{1}{2}\text{ + }\frac{1}{2}\text{ = 1} \end{gathered}[/tex]the probabilty of that it is an odd number or a number greater than 3 is 1.000 (nearest thousandth)
When a figure is translated its orientation (blank) and the measurements of its angles (blank).The options for both blanks are the same and the options are, remain the same or change
First of all, remember that translation is a transformation which doesn't imply a change of size or shape, that is, the image will be congruent to its image.
Having said that, the complete paragraph would be
When a figure is translated its orientation remains the same and the measurements of its angles remain the same.
The orientation doesn't change because it's defined as the position of points of the figure, these points change its position where we rotate the figure, which is not the case here.
if anyone could help me on #17 i would appreciate it!
Answer:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]Step-by-step explanation:
The function that was transformed is:
[tex]f(x)=\lvert x\rvert[/tex]If it reflects in the x-axis, shift 7 units to the right, and shift upward 2 units, we need to know the transformation rules for these displacements:
[tex]\begin{gathered} \text{ -f(x) reflects the function in the x-axis (upside-down)} \\ f(x-b)\text{ shifts the function b units to the right.} \\ \text{ f(x)+b shifts the function b units upward.} \end{gathered}[/tex]Now, with this in mind, the equation of the function transformed would be:
[tex]f(x)=-\lvert x-7\rvert+2[/tex]In some states, the amount of sales tax on an item is found by multiplying the cost of the item by 0.07. Find the sales tax of a DVD that costs $23.99. O $1.67 $1.68 $16.79 O $0.17
DVD = $23.99
Sales tax = (23.99 x 0.07)
= 1,679 = $1.68
The equation V=15200(0.93) t V=15200 (0.93)t represents the value (in dollars) of a car t years after its purchase
We will have the following:
[We can see a constant compound of the decrease in price]
The value of this car is decreasing at a rate of 7 percent.
The purchase price of the car was 15 200 dollars.
3 7/9 + 4 10/12 I need help
Given the fraction 3 7/9 + 4 10/12
Add the numbers first
3 + 4 = 7
Then the fractions
7/9 + 10/12
The lowest common multiple of 12 and 9 ( the denominators) is 36
Divide the denominators by 36 and multiply the result with the numerators
(7*4 + 10 * 3)/36
= (28 + 30)/36
= 58/36
= 29/18
= 1 11/18
Add this to the sum of the wholes munbers done earlier
= 7 + 1 11/18
=8 11/18
Write an equation parallel to y = 3x + 6 that passes through the point (4,7).Remember to type the" - "if a number is negative, such as-2.y =X +
The equation that is parallel to y = 3x + 6 has the same slope as y, namely 3; therefore, we already know that the equation we are seeking has the form
[tex]y=3x+b[/tex]Now we just need to solve for the y-intercept b, and to do that we use the point (4, 7 ). Putting x = 4 and y = 7 into the above equation gives
[tex]7=3(4)+b[/tex][tex]7=12+b[/tex][tex]\therefore b=-5[/tex]Hence, the equation that is parallel to y = 3x + 6 that passes through the point (4,7) is
[tex]y=3x-5[/tex]
LEARNING OBJECTIVE Determine a vertical Horizontal or oblique asymptole of a rational functionWhich of the following rational functions will have a graph with a horizontal asymptote of y=09nh7x) =2x + 4b.)4x) - 2x + 23x - 1c.)3x - 2x2x+X-1d.)2x - 83x+x+1
We need to find a vertical asymptote. This means, when we are approaching a value X, then Y becomes infinite or -infinite
A rational function R(x) = p(x) / q(x) will have a vertical asymptote at x=r when r is substituted in for x it makes the denominator zero but not the numerator
option a) oblique asymptote
option b) we have both horizontal (at y=0) and vertical (at x=-1) asymptotes
Option c)
option d) horizontal asymptote
PLS HELP WILL MARK BRAINLIEST 5 QUESTIONS
The vertex form equation is y = (x-3)^2 - 14
The equation y = x^2-6x+5 is really the equation y = 1x^2-6x+5. It is in the form y = ax^2 + bx + c where
a = 1
b = -6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -(-6)/(2*(1))
h = 6/(2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = x^2 - 6x + 5
y = -(3)^2 - 6(3) + 5
y = (9) - 6(3) + 5
y = +9-18+5
y = -4
This is the k value, so k = -4.
In summary so far, we have a = -1, h = 3 and k = -4. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = 1(x-3)^2 -4
y = (x-3)^2 - 14
Therefore the vertex form equation is y = (x-3)^2 - 14
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2. You pay $18.00 for 30 text messages. At the same rate, how much would 12text messages cost?17
$18 for 30 messages
Ratio = price / messages = 18/30
For 12 messages:
Price / messages = x /12
Equal both ratios:
18/30 = x /12
Solve for x:
0.6 (12) = x
$7.2 = x
$7.2 for 12 messages
2727. Boat Y and boat Z start traveling toward each other from 600 mile apart. Y istraveling at 35 mph, Z at 40 mph. How many hours will pass before theymeet?a. 7 b. 8 c. 9 d. 102828. Refer to problem 27. Y and Z start traveling toward each other from 600miles apart. Y is traveling at 35 mph, Z at 40 mph. How many miles will Ytravel before they meet?a. 400 b. 320 c. 350 d. 280
Given:
Speed of boat Y is 35 mph and speed of boat Z is 40 mph.
Both the boats are 600 miles a part.
I need help with my math
The Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]The graph provided suggests the use of the points (3,-3) and (5,-3). The slope is:
[tex]\displaystyle m=\frac{-3+3}{5-3}=\frac{0}{2}=0[/tex]The slope of the line is 0. It corresponds to a horizontal line
Cook-It rice cooker has a mean time before failure of 42 months with a standard deviation of 3 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 9% of the rice cookers returned? Round your answer down to the nearest whole number.
From the statement, we have a normal distribution with:
• variable X = time before failure,
,• mean μ = 42 months,
,• standard deviation σ = 3 months.
We want to know for how much time the manufacturer will not have more than 9% of the rice cookers returned. So this is equivalent to finding the value x such that the probability of failure is lower than 9%:
[tex]P(X\leq x)=9\%=0.09.[/tex]We can compute this probability using the z-scores:
[tex]\begin{gathered} P(Z\leq z)=0.09, \\ z=\frac{x-\mu}{\sigma}\Rightarrow x=\mu+\sigma\cdot z=42+3\cdot z. \end{gathered}[/tex]We have the following table for z-scores:
The entries in the table represent the area under the curve, i.e. the probability. We must look for the closest value to the probability of 0.09. From the table, we see that the closest value to this probability is 0.091:
For this value we see that we have the z-score:
[tex]z=-1.34.[/tex]Replacing this value in the equation for x from above, we get:
[tex]x=42+3\cdot(-1.34)=37.98.[/tex]So we have found that for x = 37.98, we have:
[tex]P(X\leq x=37.98)=9\%=0.09.[/tex]This means that by a time x = 37.98 months, only 9% of the cookers will fail have failed. So the manufacturer must set a warranty period of 38 months to not have more than 9% of the rice cookers returned.
AnswerThe manufacturer must set a warranty period of 38 months to not have more than 9% of the rice cookers returned.
The diameter is 16 ftwhat's the area the circle?
Explanation
Step 1
the area of a circle is given by:
[tex]\text{Area}_{circle}=\text{ }\pi\cdot\frac{diameter^2}{4}[/tex]let
diameter=16 ft
now, replace
[tex]\begin{gathered} \text{Area}_{circle}=\text{ }\pi\cdot\frac{diameter^2}{4} \\ \text{Area}_{circle}=\text{ }\pi\cdot\frac{(16ft)^2}{4} \\ \text{Area}_{circle}=\text{ }\pi\cdot\frac{256ft^2}{4} \\ \text{Area}_{circle}=201.06ft^2 \end{gathered}[/tex]I hope this helps you
The stem-and-leaf plot shows student test scores. How many students score at least 17 points?Test ScoresStem Leaf0 681 5 5 7 8 992ooooKey: 17 = 17studentsPREV2125NEXTOOO$
We are given a data set in the form of a stem and leaf plot. This means that in the stem column we have the decimal digit and in the leaf column we have the units digits.
We are asked for the number of students that have scored at least 17, this means the number of students with a score that is greater or equal to 17. From the graph those scores are:
[tex]17,18,19,19,20,20,20,20[/tex]There are 8 students that scored at least 17.
A rectangular shaped parking lot is to have a perimeter of 792 yards if the width must be 168 yards because of a building code what will the length need to be?
The perimeter of rectangular shaped parkin is P = 792 yards.
The width of rectangula parking is w = 168 yards.
The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]where l is length.
Substitute the values in the formula to determine the length of rectangular parking.
[tex]\begin{gathered} 792=2(l+168) \\ \frac{792}{2}=l+168 \\ l=396-168 \\ =228 \end{gathered}[/tex]So length need to be 228 yards.
Expand 4(y + 5).4(y+5)= 1
ANSWER
[tex]4y+20=[/tex]EXPLANATION
We want to expand the expression:
[tex]4(y+5)[/tex]To do this, we apply the distributive property:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Therefore, we have:
[tex]\begin{gathered} (4\cdot y)+(4\cdot5) \\ 4y+20 \end{gathered}[/tex]That is the answer.
what is the volume in cubic in of a cylinder with the height of 17 in and a base radius of 18in to the nearest tenth place
The volume V of a cylinder with radius r is the area of the base B (circle) times the height h . That is:
[tex]V=r^2\pi h[/tex]In our case, we have that r = 8 in and h= 17 in. Then, we have that the volume of the cylinder would be
[tex]V=r^2\pi h=(8)^2\pi(17)\text{ = }1088\pi\text{ }\approx3418,05[/tex]Then, we can conclude that the volume of the cylinder would be
3418,05 in^3
Solve the quadratic equation by completing the square.x^2+6x-1=0First choose the appropriate form and fill in the blank with the correct numbets. Then, solve the equation. Round your answer to the nerest hundredth. If there is more than one solutions, separate them with commas.
Answer:
Explanation:
Given the quadratic equation
x^2+6x-1=0
Step 1: Add 1 to both sides of the equation
x^2+6x-1 + 1 = 0 + 1
x^2 + 6x = 1
Step 2: Complete the square by adding the square of the half of coeficient of x to both sides
Coefficient of x = 6
Half of 6 = 6/2 = 3
Square of 3 = 3^2 = 9
Add 9 to both sides
x^2 + 6x + 3^2 = 1
a firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof
Problem:
A firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof?
Solution:
There are two big triangles, one of them is that formed by a fireman, the roof and the building foundation plus the height of the fireman as the vertices. So, the opposite side to the 42 degrees angle given is denoted by h_roof, and the adjacent side is 75 ft away from the building:
[tex]h_{roof\text{ }}=\text{ }75.tan(42^{\circ}\text{)}[/tex]that is:
[tex]h_{roof\text{ }}=\text{ (}75)(0.9004)\text{ = }67.53[/tex]Now, the other big triangle is formed by the fireman, the window, and the building foundation plus the height of the fireman as vertices:
[tex]h_{WIN}=75.\tan (28)[/tex]that is:
[tex]h_{WIN}=(75)(0.5317)=\text{ 39.}87[/tex]then, the difference between the heights is the roof-to-windowsill:
[tex]h=h_{roof}-h_{WIN}=\text{ }67.53-39.87\text{ = }27.66[/tex]Then, we can conclude that the correct answer is:
[tex]h=27.66[/tex]What is 3ln5x=10? I have a test
Answer:
x=e^10/3
————
5
Step-by-step explanation:
Decimal Form:x=5.60632497
Find a49 of the sequence 70,63, 56, 49, .
The 49th term of the Arithmetic Progression is -266.
The given sequence is 70,63, 56, 49,..
The given sequence is in Arithmetic Progression,
Where,
a = first term = 70,
d = common difference = 63 - 70 = -7
The general term of Arithmetic Progression is given by
[tex]a_{n} = a +(n-1)d[/tex]
Now, for n =49, the term of A.P. will be
[tex]a_{49}[/tex] = 70 + (49 -1)*(-7)
= 70 + 48*(-7)
= 70 - 336
= - 266
Hence, The 49th term of the Arithmetic Progression is -266.
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The sum of the catheters in a triangle is 27 cm. The corresponding catheter in another right-angled triangle, uniform with the first one, is 2cm and 7cm. Calculate the area of the first triangle.
Given: The sum of the catheters in a triangle is 27 cm
To Determine: The area of the triangle
Solution
Please note the below
Let the first cathetus be x, then the second cathetus would be
[tex]\begin{gathered} c_1=x \\ c_2=27-x \end{gathered}[/tex]For the second right triangle
[tex]\begin{gathered} c_1=2 \\ c_2=7 \end{gathered}[/tex]Since the two right triangles are corresponding to each other, then the ratio of their cathethers are equal
Therefore
[tex]\begin{gathered} \frac{x}{27-x}=\frac{2}{7} \\ 7x=2(27-x) \\ 7x=54-2x \\ 7x+2x=54 \\ 9x=54 \\ x=\frac{54}{9} \\ x=6 \end{gathered}[/tex]So, the cathethers for the first right triangle would be
[tex]\begin{gathered} c_1=x:c_2=27-x \\ c_1=6 \\ c_2=27-6 \\ c_2=21 \end{gathered}[/tex]Note that the catheters formed the base and the height of the first triangle. The area of a triangle can be calculated using the formula below
[tex]\begin{gathered} Area(triangle)=\frac{1}{2}\times base\times height \\ Area(triangle)=\frac{1}{2}\times6cm\times21cm \\ Area(triangle)=3cm\times21cm \\ Area(triangle)=63cm^2 \end{gathered}[/tex]Hence, the area of the first triangle is 63cm²
What is the probability that a customer selected at random was male and purchased a SUV?
Given:
A table
Required:
The probability that a customer selected at random was male and purchased an SUV.
Explanation:
The probability of getting a male with an SUV is given by
The total number of males divided by the total number of people and multiply by the number of SUVs divided by the total number of cars
[tex]\frac{60}{240}\times\frac{21}{240}=0.021875[/tex]Final Answer:
0.021875
solve the system of linear equations by elimination x+2y=13 -x+y=5
To solve the system
[tex]\begin{gathered} x+2y=13 \\ -x+y=5 \end{gathered}[/tex]we add the two equations to get:
[tex]\begin{gathered} x+2y=13 \\ -x+y=5 \\ --------------_{} \\ 0+3y=18 \end{gathered}[/tex]Dividing both sides by 3 gives
[tex]y=6[/tex]with the value of y in hand, we now put it in -x + y = 5 to get
[tex]-x+6=5[/tex]subtracting 6 from both sides gives
[tex]-x=-1[/tex][tex]x=1[/tex]Hence, the solution to the system is
[tex]\begin{gathered} x=1 \\ y=6. \end{gathered}[/tex]Time(wki469Height ofplant (in)9.013.520.25Find the rate of change for weeks 40le and 69.Explain the meaning of the rate of change for each case.
Explanation
Step 1
when you have 2 coordinates ( A and B), the slope of the line that passes thought those point is given by
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} A=(x_1,y_1) \\ B=(x_2,y_2) \end{gathered}[/tex]A and B are 2 known points of the line
Step 2
so, the slope represents the rate of change
i)the rate of change for 4-6 weeks
Let
A=(4 ,9)
B=(6,13.5)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{13.5-9}{6-4}=\frac{4.5}{2}=2.25 \\ slope_1=2.25 \end{gathered}[/tex]Step 3
ii)the rate of change for 6-9weeks
Let
A(6,13.5)
B(9,20.25)
replace,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{20.25-13.5}{9-6}=\frac{6.75}{3}=2.25 \end{gathered}[/tex]the slope represents the rate of change, it means for every case the plant is growing at a constant rate (2.25 inches per week)
I hope this helps you
Hi, can you help me with this problem?A manufacturer has a monthly fixed cost of $42,500 and a production cost of $6 for each unit produced. The product sells for $11/unit.(a) What is the cost function?C(x)= (b) What is the revenue function?R(x)=(c) What is the profit function?P(x)= (d) Compute the profit (loss) corresponding to production levels of 6,000 and 11,000 units.P(6,000)=P(11,000)=
Given:
Fixed cost = b = $ 42,500
Production cost (Variable cost) /unit = m = $ 6/ unit
Let 'x' represent the number of unit, therefore the variable cost will be
[tex]6x[/tex]a) The cost function will be the sum of the fixed cost and the variable cost.
[tex]C(x)=6x+42500[/tex]b) The revenue function is the amount the product is sold per unit.
Recall: 'x' represents the number of units.
Therefore,
[tex]11\times x=11x[/tex]Hence, the revenue function R(x) is
[tex]R(x)=11x[/tex]c) The profit function is the difference between the revenue function and the cost function.
[tex]P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500[/tex]Hence, the profit function is
[tex]P\mleft(x\mright)=5x-42500[/tex]d) Let us compute the profit (loss) values when the units are 6000 and 11000
Using the profit function
[tex]P(x)=5x-42500[/tex]Therefore,
[tex]\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} P(6000)=-\text{ \$12500 (which is a loss)} \\ P(11000)=\text{ \$12500 (this is a profit)} \end{gathered}[/tex]2. A right prism has a square base of edge a and altitude h, write the formula for the total surface area
Given the shape in the question the total surface area of a prism is given by:
[tex]\begin{gathered} ph+2A \\ \text{where p=perimeter of the base} \\ h=\text{height} \\ A=\text{Area of the base} \end{gathered}[/tex]Since the right prism is square based, then we have:
[tex]\begin{gathered} \text{perimeter of a square = 4a where a is the edge of the square} \\ \text{Area of a square= a}^2 \end{gathered}[/tex]Hence, the formula for the total surface area of the prism is given by:
[tex]\begin{gathered} 4ah+2a^2 \\ \text{where a is the edge of the square and h is the height} \end{gathered}[/tex]Managers of a sports arena’s parking garage keep track of the duration of time customers park their cars there. Shown in the stem and - leaf display below is a sample of 15 such parking duration (in minutes). Use the display to answer the questions that follow.
Step 1
A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
[tex]198\text{ Minutes}[/tex]Step 2
[tex]\begin{gathered} In\text{ the 180s, we have;} \\ 182,183,186,189\text{ minutes} \\ The\text{ shortest parking duration in the 180's is 182} \\ Answer=182\text{ Minutes} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} In\text{ the 160's, we have; 160,164,164} \\ Answer=3\text{ } \end{gathered}[/tex]if m=24 and v=4 p=mv
p = 96 is the product of m = 24 and v = 4
What is multiplication ?In mathematics, a product is the outcome of multiplication, or an expression that identifies the things to be multiplied, known as factors.
Calculationm = 24
v = 4
p = mv
p = 24 * 4 = 96
p = 96
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