The linear equation parallel to line u that passes through (7,9) is y = 2x - 5
How to find the equation of line V?
Two lines are parallel if have the same slope, we know that line V is parallel to:
y = 2x + 8/9
Then line V will be of the form:
y = 2x + c
To find the value of c, we use the fact that the line passes through (7, 9), replacing these values we get:
9 = 2*7 + c
9 = 14 + c
9 - 14 = c
-5 = c
The linear equation is y = 2x - 5
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Given points C(-3,-8) and D(-6.5,-4.5), find the coordinate of the point that is 2/3 of the way from C to D.
Answer:
(-16/3,-17/3)
Explanation:
Let the point which is 2/3 of the way from C to D = X
It means that point X divides the line segment CD internally in the ratio 2:1.
To determine the coordinate of point X, we use the section formula for internal division of a line segment:
[tex](x,y)=\left\{ \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right\} [/tex][tex]\begin{gathered} (x_{1,}y_1)=(-3,-8) \\ (x_2,y_2)=(-6.5,-4.5) \\ m\colon n=2\colon1 \end{gathered}[/tex]Substituting these values into the formula above, we have:
[tex]X(x,y)=\left\{ \frac{2(-6.5)+1(-3)}{2+1},\frac{2(-4.5)+1(-8)}{2+1}\right\} [/tex]We then simplify:
[tex]\begin{gathered} X(x,y)=\left\{ \frac{-13-3}{3},\frac{-9-8}{3}\right\} \\ =\left\{ \frac{-16}{3},\frac{-17}{3}\right\} \end{gathered}[/tex]Therefore, the exact coordinate of the point that is 2/3 of the way from C to D is (-16/3,-17/3).
I need a tutor for algebra
Answer:
0.40
Explanation:
From the question, we're given that;
* 8% of the members run only long-distance, so the probability that a member of the team will run only long-distance, P(A) = 8/100 = 0.08
* 12% compete only in non-running events, so the probability that a member will compete only in non-running events, P(B) = 12/100 = 0.12
* 32% are sprinters only, so the probability that a member is a sprinter only P(C) = 32/100 = 0.32
We're asked in the question to determine the probability that a randomly chosen team member runs only long-distance or competes only in sprint events, since these events cannot occur at the same time, we can use the below formula to solve as shown below;
[tex]P(\text{A or C) = P(A) + P(C)}[/tex]P(A or C) = 0.08 + 0.32 = 0.40
A)As the x-value Increases by one, the y-value decreases by 2.26.B)As the x-value increases by one, the y-value decreases by 53.769.C)As the x-value Increases by one, the y-value increases by 2.26.D)As the x-value Increases by one, the y-value Increases by 53.769. Which equation describes the line of best fit for the table below?
Option A
Explanations:The graph shows an inverse proportion.
As x increases, y decreases in value.
Finding the slope of the graph:
dy / dx = (y₂ - y₁) / (x₂ - x₁)
x₁ = 5, x₂ = 9, y₁ = 40, y₂ = 30
dy / dx = (30 - 40) / (9 - 5)
dy / dx = -10 / 4
dy / dx = -2.5
This means that as x increases by 1, decreases by 2.5
A is the only correct option.
find the value of X and y if l || m.
The Solution.
Step 1:
We shall find two equations from the given angles.
First, by vertically opposite angle property of angles between two lines, we have that:
[tex]\begin{gathered} 7y-23=23x-16 \\ \text{Collecting the like terms , we get} \\ 7y-23x=23-16 \\ 7y-23x=7\ldots.eqn(1) \end{gathered}[/tex]Similarly, by alternate property of angles between lines, we have that:
[tex]\begin{gathered} 23x-16+8x-21=180 \\ \text{Collecting like terms, we get} \\ 31x-37=180 \\ 31x=180+37 \\ 31x=217 \\ \text{Dividing both sides by 31, we get} \\ x=\frac{217}{31}=7 \end{gathered}[/tex]Step 2:
We shall find the values of y by substituting 7 for x in eqn(1), we get
[tex]\begin{gathered} 7y-23(7)=7 \\ 7y-161=7 \\ 7y=7+161 \\ 7y=168 \\ \text{Collecting the like terms, we get} \\ y=\frac{168}{7}=24 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
The correct answers are; x = 7 , and y = 24
A/ Question 8 (5 points) A recent Nielson rating poll contact a random sample of Americans to determine the amount of time their family watched television on a Tuesday night. Exactly 250 people were involved in the poll with 37 people watching no television. 51 people watching 30 minutes of television. 17 people watching 45 minutes of television. 20 people watching 60 minutes of television, 19 people watching 75 minutes of television. 11 people watching 90 minutes of television. 50 people watching 120 minutes of television, and 45 people watching 240 minutes of television. Determine the mode from the given Nielson rating poll.
Answer
The mode of the Nielsen rating poll is the group that watch 30 minutes of televison.
Explanation
The mode in a dataset is the variable with the highest frequency. That is, the variable that occurs the most in the dataset.
37 people watching no television.
51 people watching 30 minutes of television.
17 people watching 45 minutes of television.
20 people watching 60 minutes of television.
19 people watching 75 minutes of television.
11 people watching 90 minutes of television.
50 people watching 120 minutes of television.
45 people watching 240 minutes of television.
The group with the highest frequency (51) is the the group that watch 30 minutes of television.
Hope this Helps!!!
solve the inequality for h. h-8> 4h+5. write the answer in simplest form
Subtract '4h' from both RHS (Right-Hand side) and LHS of the inequality (Left-Hand side).
[tex]\begin{gathered} h-8-4h>4h+5-4h \\ (h-4h)-8>5+(4h-4h) \\ -3h>5 \end{gathered}[/tex]Add '8' on both LHS and RHS of the above expression.
[tex]undefined[/tex]Divide both RHS and LHS of the above expression with '-3'. Whenever an inequality is divide or multiple with a negative value, the sign of the inequality shifts. Here, the above expression is dividing with '-3'. Thus, the > symbol shifts to < symbol.
[tex]\begin{gathered} \frac{-3h}{-3}<\frac{5}{-3} \\ h<\frac{-5}{3} \end{gathered}[/tex]Thus, the iniequality for h is h<-(5/3).
What are the solutions to the equation ? e^1/4x = (4x) [tex]e^1/4x =abs( 4x)[/tex](Round to the nearest hundredth). The solutions are about x = and
The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given expression,
e^(x/4) = |4x|
The function e^(x/4) is an exponential function and the plot of this function has been plotted below.
The mode function |4x| has also been plotted below.
The point of intersection is the point where both will be the same or the solution meets.
The first point of intersection is (0.267,1.0691) so x = 0.267 ≈ 0.27
The second point of intersection (-0.2357,0.9428) so x = -0.2357 ≈ -0.24
Hence " The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.".
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A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
Let
x -----> number of boys
y -----> total number of children
we have that
x=11 -----> given
y=21 ----> given
therefore
The fraction of the class that is made up of boys is equal to
x/y
substitute
11/21A farm raises cows and chickens. The farm has total of 43 animals. One day he counts the legs of all his animals and realizes he has a total of 122. How many cows and chickens does he have?
Assume that there are x cows and y chickens in the form
Since there are 43 animals, then
Add x and y, then equate the sum by 43
[tex]x+y=43\rightarrow(1)[/tex]Since a cow has 4 legs and a chicken has 2 legs
Since there are 122 legs, then
Multiply x by 4 and y by 3, then add the products and equate the sum by 122
[tex]4x+2y=122\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -2 to make the coefficients of y equal in values and opposite in signs
[tex]\begin{gathered} -2(x)+-2(y)=-2(43) \\ -2x-2y=-86\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate y
[tex]\begin{gathered} (4x-2x)+(2y-2y)=(122-86) \\ 2x+0=36 \\ 2x=36 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]Substitute x by 18 in equation (1)
[tex]18+y=43[/tex]Subtract 18 from each side
[tex]\begin{gathered} 18-18+y=43-18 \\ y=25 \end{gathered}[/tex]The answer is
There are 18 cows and 25 chickens on the farm
nction.
f(x) = -x² + 3x + 11
Find f(-1)
Answer:
f(-1) = 7
Step-by-step explanation:
Hello!
You can evaluate for f(-1) by substituting -1 for x in the equation.
Evaluate f(-1)f(x) = -x² + 3x + 11f(-1) = -(-1)² + 3(-1) + 11f(-1) = -1 -3 + 11f(-1) = -4 + 11f(-1) = 7f(-1) is 7.
Answer:
f(-1) = 7
Step-by-step explanation:
Hello!
You can evaluate for f(-1) by substituting -1 for x in the equation.
Evaluate f(-1)f(x) = -x² + 3x + 11f(-1) = -(-1)² + 3(-1) + 11f(-1) = -1 -3 + 11f(-1) = -4 + 11f(-1) = 7f(-1) is 7.
you are packing for a road trip and want to figure out how much you can fit in your rectangular suitcase the suitcase has the following dimensions list length2 1/3ft width 1/3ft 1 1/2ft what is the volume of your suitcase in cubic feet
The Volume of the suitcase is given by the formula:
Length x width x height = L X W X H
L= 2 1/3ft
W= 1/3ft
H= 1 1/2ft
[tex]\begin{gathered} \text{Volume = 2}\frac{1}{3\text{ }}\text{ x }\frac{1}{3}\text{ x 1}\frac{1}{2}ft^3 \\ V\text{ = }\frac{7}{3}\text{ x }\frac{1}{3}\text{ x}\frac{3}{2}ft^3 \\ V\text{ = }\frac{21}{18}ft^3 \\ V=\text{ }\frac{7}{6}ft^3 \\ V=\text{ 1}\frac{1}{6}ft^3 \end{gathered}[/tex]Volume of the suitcase is 1 1/6 cubic feet
Explain how rays AB and AC form both a line and an angle.
Answer:
The point from C goes straight until it reaches A and stull continues till it gets ti B and stops. The angle is then given as 180°
An Integer is a number with a fractional part. True or False
An integer is a number with a fractional part is true statement.
Can someone help me with this geometry question? First box has 3 options: 60,96,48Second box has two options: 480 and 552Third box: 180 and 216
Surface area of a square prism is:
[tex]\begin{gathered} \text{4\lparen ah\rparen= SA square prism} \\ 4(20)(6)\text{= SA square prism} \\ 80(6)\text{= SA square prism} \\ 480=\text{SA square prism} \\ \\ \end{gathered}[/tex]The surface area of the square prism 480.
The surface area for the cube is:
[tex]\begin{gathered} 5a^2=\text{ SA cube} \\ 5(6)^2=\text{ SA cube} \\ 5(36)=\text{ SA cube} \\ 180=\text{ Surface area of the cube} \end{gathered}[/tex]The surface area of the cube is: 180.
The surface area of the pyramid is:
[tex]\begin{gathered} SurfaceAreaPyramid=4bh \\ SAPyramid=\text{4\lparen6\rparen\lparen4\rparen} \\ SAPyramid=\text{ 96} \\ \end{gathered}[/tex]The surface area of the pyramid i 96.
In each geometric figure, we have to remove the inner square faces, since they are not on the surface.
The total surface area is:
[tex]\begin{gathered} SA\text{ cube + SA square prism + SA pyramid= Total SA} \\ 180\text{ + 480 + 96= Total SA} \\ 756=\text{ Total surface area. } \end{gathered}[/tex]The total surface area is 756.
Describe the features of the function that can be easily seen when a quadratic function is givenin the form: y = ax2 + bx + c and how they can be identified from the equation. How can thisform be used to find the other features of the graph?
Hello there. To solve this question, we need to remember some properties about quadratic functions and its key features.
Let f(x) = ax² + bx + c, for a not equal to zero.
The main key feature we can see at first glance is the leading coefficient a.
If a < 0, the parabola (the graph of the function) will have its concavity facing down.
If a > 0, the parabola will have its concavity facing up.
It also means the function will have either a maximum or a minimum point on its vertex, respectively.
Another key feature of the function is the y-intercept, i. e. the point in which the x-coordinate is equal to zero, is (0, c).
The x-intercepts of the graph (in plural), are the roots of the function.
If b² - 4ac > 0, we'll have two distinct real roots.
If b² - 4ac = 0, we'll have two equal real roots.
If b² - 4ac < 0, we'll have two conjugate complex roots (not real roots)
This b² - 4ac is the discriminant of the function.
The roots can be found by the formula:
x = (-b +- sqrt(b² - 4ac))/2a
The vertex of the graph can be found on the coordinates (xv, yv), in which xv is calculated by the arithmetic mean of the roots
xv = ((-b + sqrt(b²-4ac))/2a + (-b-sqrt(b²-4ac))/2a)/2 = -b/2a
The yv coordinate can be found by plugging in xv in the function
yv = a(-b/2a)² + b(-b/2a) + c, which will be equal to -(b²-4ac)/4a.
help meee pleaseeee pleasee
Answer:
f(x) = (-1/4)x - 5
Step-by-step explanation:
(-8, -3), (-12, -2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -2 - (-3) -2 + 3 1 -1
m = ------------ = ------------- = ----------- = --------- = -------
x₂ - x₁ -12 - (-8) -12 + 8 -4 4
y - y₁ = m(x - x₁)
y - (-3) = (-1/4)(x - (-8)
y + 3 = (-1/4)(x + 8)
y + 3 = (-1/4)x - 2
-3 -3
-------------------------------
y = (-1/4)x - 5
I hope this helps!
If 16 is increased to 23, the increase is what percent of the original number? (This is known as the percent of change.)
Step 1
Given data
Old value = 16
New value = 23
Step 2
Write the percentage increase formula
[tex]\text{Percentage increase = }\frac{I\text{ncrease}}{\text{Old}}\text{ }\times\text{ 100\%}[/tex]Step 3
Increase = 23 - 16 = 7
[tex]\begin{gathered} \text{Percentage increase = }\frac{7}{16}\text{ }\times\text{ 100\%} \\ =\text{ 43.75\%} \end{gathered}[/tex]Write an equation for the inverse variation represented by the table.x -3, -1, 1/2, 2/3y 4, 12, -24, -18
By definition, Inverse variation equations have the following form:
[tex]y=\frac{k}{x}[/tex]Where "k" is the Constant of variation.
Given the values shown in the table, you can find the value of "k":
- Choose a point from the table. This could be:
[tex](-3,4)[/tex]Notice that:
[tex]\begin{gathered} x=-3 \\ y=4 \end{gathered}[/tex]- Substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{-3} \\ \\ (4)(-3)=k \\ k=-12 \end{gathered}[/tex]Knowing the Constant of variation, you can write the following equation:
[tex]y=\frac{-12}{x}[/tex]The answer is:
[tex]y=\frac{-12}{x}[/tex]If we use 3.14 for pi, describe the ratio between the circumference and the diameter of a circle.
Solution
The ratio of the circumference of any circle to the diameter of that circle.
[tex]\begin{gathered} \text{circumference of a circle=}\pi d \\ \text{where d is the diameter} \\ \\ \text{circumference of a circle=3.14}d \end{gathered}[/tex]The ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi.
8in 8in 8in area of irregular figures
Given data:
The given figure.
The expression for the area is,
[tex]\begin{gathered} A=(8\text{ in)(8 in)+}\frac{1}{2}(8\text{ in)( 8 in)} \\ =96in^2 \end{gathered}[/tex]Thus, the area of the given ffigure is 96 square-inches.
Evaluate. 7⋅5+42−23÷4
The result that can be gotten from the evaluation here is 6.625
How to solve the problemWe would have to solve the problem following the order that the operations are. The reason why it would have to be solve this way is because the operations are not in a bracket.
If it was in brackets, the brackets would have to be solved first using the bodmas rule
so we would have
7⋅5+42 = 49.5
49.5 - 23 = 26.5
26.5 / 4 = 6.625
The value that we got from the evaluation is 6.625
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Help me to answer this question with vectors, thank you
To find:
The coordinates of a point P such that PA = PB.
Solution:
Given that A(4, 0) and B(0, 9) are the coordinates.
Let the point P is (x,0) because the point is on x-axis, and it is given that |PA| = |PB|.
So,
[tex]\sqrt{(4-x)^2+(0-0)^2}=\sqrt{(x-0)^2+(0-9)^2}[/tex]Now, squaring both the sides:
[tex]\begin{gathered} (4-x)^2=x^2+9^2 \\ 16+x^2-8x=x^2+81 \\ 8x=-65 \\ x=\frac{-65}{8} \end{gathered}[/tex]Thus, the coordinates of point P are (-65/8, 0).
Use function composition to verify f(x)=-3x+5 and g(x)=5x-3 are inverses. Type your simplified answers in descending powers of x an do not include any spaces between your characters.Type your answer for this composition without simplifying. Use parentheses to indicate when a distribution is needed to simplify. g(f(x))=AnswerNow simplify the composition, are f(x) and g(x) inverses? Answer
Answer:
• (a)g[f(x)]=5(-3x+5)+5
,• (b)No
Explanation:
Given f(x) and g(x):
[tex]\begin{gathered} f(x)=-3x+5 \\ g(x)=5x-3 \end{gathered}[/tex](a)First, we find the composition, g[f(x)].
[tex]\begin{gathered} g(x)=5x-3 \\ \implies g\lbrack f(x)\rbrack=5f(x)-3 \\ g\lbrack f(x)\rbrack=5(-3x+5)+5 \end{gathered}[/tex](b)Next, we simplify g[f(x)] obtained from part (a) above.
[tex]\begin{gathered} g\mleft[f\mleft(x\mright)\mright]=5\mleft(-3x+5\mright)+5 \\ =-15x+25+5 \\ =-15x+30 \end{gathered}[/tex]Given two functions, f(x) and g(x), in order for the functions to be inverses of one another, the following must hold: f[g(x)]=g[f(x)]=x.
Since g[f(x)] is not equal to x, the functions are not inverses of one another.
What is the product of 125 × 25
Answer:
Step-by-step explanation:
125 X 25
= 3,125
Silvergrove Hardware kept an inventory of 517,110 lawnmowers in the past. With a change inmanagement, the hardware store now keeps an inventory of 70% more lawnmowers. Howmany lawnmowers is that?
879,087.
EXPLANATION
To find the number of lawnmowers, we need to first find 70% of the number of lawnmowers that was kept in the past. Then add the to the number of lawnmowers kept in the past.
From the given question;
Number of lawnmowers kept in the past = 517, 110.
70% of lawnmowers kept in the past = 70% of 517 110
[tex]\begin{gathered} =\frac{70}{100}\times517\text{ 110} \\ \\ =361\text{ 977} \end{gathered}[/tex]Number of lawnmowers now kept in store = number of lawnmowers kept in the past + 70% of lawnmowers kept in the past
= 517 110 + 361 977
= 879,087.
Find the percent of change from 120 bananas to 40 bananas.
Answer:
67% decrease
Explanation:
From the given problem:
Initial number of bananas = 120
Final number of bananas = 40
[tex]\begin{gathered} \text{Percent Change=}\frac{Final\text{ Value-Initial Value}}{\text{Initial Value}}\times100 \\ =\frac{40-120}{120}\times100 \\ =-\frac{80}{120}\times100 \\ =-0.667\times100 \\ =-66.7\% \\ \approx-67\% \end{gathered}[/tex]Since we have a negative value, we have a 67% decrease.
What is the length of the side adjacent to angle 0?
To answer this question, we always need to take into account the reference angle in a right triangle. The reference angle here is theta, Θ, and we have that:
Then, the length of the side adjacent to theta is equal to 15.
In summary, we have that the length of the side adjacent to the angle Θ is equal to 15.
How do I solve this problem?Mary reduced the size of a painting to a width of 3.3 inches. What is the new height of it was originally 32.5 inches tall and 42.9 inches wide? Round your answer to the nearest tenth.
Given the follow equivalence
[tex]\frac{Oldwidth}{Oldheight}=\frac{Newwidth}{Newheight}[/tex]where
old width=42.9
Old height= 32.5
New width=3.3
then
[tex]\frac{42.9}{32.5}=\frac{3.3}{Newheight}[/tex][tex]Newheight=3.3*\frac{32.5}{42.9}[/tex][tex]Newheight=2.5[/tex]New height is 2.5 inches
What is the sum of -15 + 182A. 33B. 3c. -3 D-33Your answer
-15 + 18 is the same as 18 - 15, which is equal to 3.
A company estimates that that sales will grow continuously at a rate given by the functions S’(t)=15e^t where S’(t) Is the rate at which cells are increasing, in dollars per day, on day t. find the sales from the 2nd day through the 6th day (this is the integral from one to six)
Given the function:
[tex]S^{\prime}(t)=15e^t[/tex]Where S’(t) Is the rate at which sales are increasing (in dollars per day). To find the sales from the second day through the 6th day, we need to integrate this function from t = 1 to t = 6:
[tex]\int_1^6S^{\prime}(t)dt=\int_1^615e^tdt=15\int_1^6e^tdt[/tex]We know that:
[tex]\int e^tdt=e^t+C[/tex]Then:
[tex]15\int_1^6e^tdt=15(e^6-e^1)\approx\text{\$}6010.66[/tex]The sales from the 2nd day through the 6th day are $6,010.66