Solution:
Given the ordered pairs;
[tex]\lbrace(-13,9),(-7,-5),(5,14),(11,-10)\rbrace[/tex]The domain, x, of the function is;
[tex]x=\lbrace-13,-7,5,11\rbrace[/tex]Then, the range, y, is;
[tex][/tex]7. A line passes through (2, -1) and (8, 4). Writean equation for the line in point-slope form.Rewrite the equation in standard form using integers.y + 1 = %(x+ 2); -5x + 6y = -16•y-1=2(0x-2); -5x+ 6y= 16y-2=%0x+1);-5x+ 6y=17•y+1= %k-2);-5x+ 6y= -16
Recall that the equation of a line that passes through two points is given by the following formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Notice that the above formula gives us the equation of the line in point-slope form. Substituting the given values in the above formula, we get:
[tex]y-(-1)=\frac{-1-4}{2-8}(x-2).[/tex]Simplifying the above result, we get:
[tex]y+1=\frac{5}{6}(x-2).[/tex]Now, taking the above equation to its standard form, we get:
[tex]\begin{gathered} 6y+6=5(x-2), \\ 6y+6=5x-10, \\ 6y-5x=-10-6, \\ -5x+6y=-16. \end{gathered}[/tex]Answer: [tex]y+1=\frac{5}{6}(x-2);-5x+6y=-16.[/tex]Two points determine a line. Find an equation of the line passing through the points.
(2,−7) and (5,−19)
An equation of the line is y=
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{-19 +7}{3} \implies \cfrac{ -12 }{ 3 } \implies - 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- 4}(x-\stackrel{x_1}{2}) \implies y +7 = - 4 ( x -2) \\\\\\ y+7=-4x+8\implies {\Large \begin{array}{llll} y=-4x+1 \end{array}}[/tex]
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Other than the unit of measurement i am genuinely confused by this because (as far as I know) there is no possible way of figuring this out. The unit is obviously meters but I have no idea what the answer is. You should ask your teacher to explain it to you because it's confusing.
can you help me with the fourth one marked as e
we have the equatiion
4x-5y=20
Convert to slope intercept form
y=mx+b
so
Isolate the variable y
step 1
subtract 4x both sides
4x-5y-4x=4x+20
simplify
-5y=-4x+20
step 2
Divide both sides by -5
so
-5y/-5=(-4x+20)/-5
simplify
y=(4/5)x-4What is the answer to this
Answer:
38.461538
Step-by-step explanation:
Find the real zeros of f (x) =45x -5x^3
We will have the following:
[tex]f(x)=45x-5x^3\Rightarrow f(x)=-5x(x^2-9)[/tex][tex]\Rightarrow f(x)=-5x(x-3)(x+3)[/tex]So, its zeros are x = -3, x = 0 & x = 3.
How can I draw a vertical bar chart to represent the recorded data shown above using the approximate heights in metres where necessary?
Hello!
As this exercise informs the approximate heights, you can consider just this value (don't need to write two heights in this case).
To make this chart, I used the heigths:
• Mercedario: 6770m
,• Misti, Volcán: 5820m
,• Pular: 6230m
,• Sajama: 6520m
,• Talima: 5220m
Look at the chart below:
Solve the compound inequality.2x-5 33 and 3x-12-19Graph the solution on the number line:
Consider the system of inequalities,
[tex]\begin{gathered} 2x-5\leq3 \\ 3x-1\ge-19 \end{gathered}[/tex]Simplify the first inequality as follows,
[tex]\begin{gathered} 2x-5+5\leq3+5 \\ 2x\cdot\frac{1}{2}\leq8\cdot\frac{1}{2} \\ x\leq4 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.
Simplify the second inequality as follows,
[tex]\begin{gathered} 3x-1+1\ge-19+1 \\ 3x\cdot\frac{1}{3}\ge-18\cdot\frac{1}{3} \\ x\ge-6 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.
The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.
The solution can be seen on the number line as follows,
identify the area od the rhombus.
Calculate the height of the upper triangle, using the Pythagoras theorem
[tex]\begin{gathered} 25^2=7^2+h^2 \\ h^2\text{ = }625\text{ - 49} \\ h^2\text{ = }576 \\ h\text{ = }\sqrt[]{576} \\ h\text{ = }24 \end{gathered}[/tex]The length of the vertical diagonal = 2 x 24
The length of the vertical diagonal = 48m
[tex]\begin{gathered} \text{Area = }\frac{48\times14}{2} \\ \text{Area = }48\times7 \\ \text{Area = 336 m}^2 \end{gathered}[/tex]PLEASE HELP, Simplify: 4/9+3/7
Answer:
7/16
Step-by-step explanation:
To find the answer, simply just add the numbers together:
For the numerators:
4 + 3 = 7
For the denominators:
9 + 7 = 16
So, we have 7/16 because this cannot be simplified down anymore.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
Exact Form:
55/63
Decimal Form:
¯¯¯¯¯¯¯¯¯¯¯¯
0.873015
Step-by-step explanation:
a) what are the coordinates of points P and Q?b)Evaluate f(b)c) solve f(x)=e for xd)suppose c=f(z) and z=f(x).what is x?e) suppose f(b)=-f(d).what additional information does this give you?
a) Remember that the coordinates for any given point in the cartesian system have two components, one in the X axis and the secon one in the Y axis. (X,Y)
The coordinates for P and Q are:
P (b,a)
Q(d,e)
b) If you have the formula for the function, you'll se that to determine the value on the Y axis for a given value of X you have to replace that value in the formula. This means that Y= f(x).
In this example the value of Y for X=b is equal to a, so f(b)= a
c) For f(x)=e, you have to identify the value of x that croses to Y=e, in this grapfic that value is d
d) f(z)=c and f(x)=z
If you watch the graphic, c is in the y-axis, this means that the x value of its coordinate is zero. So z=0
Now for f(x)=z, this means that you have to find the value of x when the value of Y is zero. To determine this value you have to see where the function crosses the X-axis.
The function crosses the X-axis in point h, so when f(x)= z, x=h
e) If f(b)=-f(d) this means that both |b| and |d| are equal, you can express it as:
b=-d
Pls do this for me asap
Answer:
The correct answer is B
Step-by-step explanation:
What equation below has a linear graph that is parallel to the graph of y 2 on the Cartesian coordinate system
x=2
y=7
y=-2r
y=2r
Answer:
x=2
Step-by-step explanation:
The required equation x = 2 has a linear graph that is parallel to the graph of the y-axis on the Cartesian coordinate system. which is the correct answer would be option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A vertical line is a line on the coordinate plane with all of its points having the same x-coordinate. When we plot the points for a function x = an on a coordinate plane, we discover that connecting the coordinates results in a vertical line.
As per the given question, we have
The required equation x = 2 is the required vertical line.
Thus, the required equation x = 2 has a linear graph that is parallel to the graph of the y-axis on the Cartesian coordinate system.
Hence, the correct answer would be an option (A).
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a circular field has area 14400 square feet what is the radius? a 12ft b 120ft c 720ft d 7200ft
The radius of the circular field with area 14400 square feet is 67.7ft
What is a circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
The radius of a circular field with an area of 14400 square feet can be calculated by the formula:
Area of a circle(A) = [tex]\pi r^{2}[/tex]
where A = 14400[tex]ft^{2}[/tex]
[tex]\pi[/tex] = constant which is 3.142
A = [tex]\pi[/tex][tex]r^{2}[/tex], where A = area of circle , r = radius
divide both sides by c
A/[tex]\pi[/tex] = [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = A/[tex]\pi[/tex]
r = [tex]\sqrt{\frac{A}{\pi } }[/tex]
Substitute the values of A and [tex]\pi[/tex]
r = [tex]\sqrt{\frac{14400}{3.142} }[/tex]
r = 67.7ft
In conclusion the radius of the field is 67.7ft
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For a certain company , the cost for producing items is 45x + 300 and the revenue for selling items is 85x - 0.5x ^ 2. Part a: set up an expression for the profit from producing and selling x items and solve. we assume the company sells all of the items it produces. Part B: find two values of x thatvwill create a profit of $50. Part C: is it possible for the company to make a profit if $2500?
Producing cost:
[tex]45x+300[/tex]Revenue:
[tex]85x-0.5x^2[/tex]The profit (P) is equal to substract the producing cost for the revenue:
[tex]\begin{gathered} P=(85x-0.5x^2)-(45x+300) \\ P=85x-0.5x^2-45x-300 \\ P=40x-0.5x^2-300 \end{gathered}[/tex]
You can write also as:
[tex]P=-0.5x^2+40x-300[/tex]----------------------------------
P=50:
[tex]50=-0.5x^2+40x-300[/tex]To solve for x:
Substract 50 in both sides of the equation:
[tex]\begin{gathered} 50-50=-0.5x^2+40x-300-50 \\ 0=-0.5x^2+40x-350 \end{gathered}[/tex]Use the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-40\pm\sqrt[]{40^2-4(-0.5)(-350)}}{2(-0.5)} \\ \\ x=\frac{-40\pm\sqrt[]{1600-700}}{-1} \\ \\ x=\frac{-40\pm\sqrt[]{900}}{-1} \\ \\ x=\frac{-40\pm30}{-1} \\ \\ x_1=\frac{-40+30}{-1}=\frac{-10}{-1}=10 \\ \\ x_2=\frac{-40-30}{-1}=\frac{-70}{-1}=70 \end{gathered}[/tex]Then, the two values of x that make a profit of $50 are: 10 and 70------------------ ----------------------
P=2500
[tex]2500=-0.5x^2+40x-300[/tex]Solve for x:
[tex]\begin{gathered} 0=-0.5x^2+40x-300-2500 \\ 0=-0.5x^2+40x-2800 \\ \\ x=\frac{-40\pm\sqrt[]{40^2-4(-0.5)(-2500)}}{2(-0.5)} \\ \\ x=\frac{-40\pm\sqrt[]{1600-5000}}{-1} \\ \\ x=\frac{-40\pm\sqrt[]{-34000}}{-1} \end{gathered}[/tex]As the number under the square root is a negative number the equation has no solution (value of x) in the real numbers.
No, is not possible for the company to make a profit of $2500Urgent need of help!
The measure of the angle ∠ABD is calculated as 138° from the given data and figure.
What is triangle's angle sum property?The total of a triangle's three internal angles is 180 degrees, according to the angle sum property. When the values of the other two angles are known, the angle sum property is utilized to compute the measure of an unknown interior angle.
What exactly is the SAS rule of similarity?SAS stands for Side-Angle-Side Similarity. If the proportion of the two sides of one triangle is the same as the proportion of the two sides of another triangle, and the angle inscribed by the two sides of both triangles is equal, two triangles are said to be similar.
Given: ΔACD and ΔBCD are isosceles.
AD ≅ AC
BD ≅ BC
∠BAC = 18°
∠BDC = 48°
We need to determine the measure of ∠ABD.
Since, AD ≅ AC
∠DAB = ∠BAC = 18°
Since, BD ≅ BC
∠BDC = ∠BCD = 48°
By triangle's angle sum property,
∠BDC + ∠BCD + ∠DBC = 180°
48° + 48° + ∠DBC = 180°
∠DBC = 84°
Also, ∠ABD = ∠ABC [By SAS rule of ΔABD + ΔABC]
From the figure we can see that,
∠DBC + ∠ABD + ∠ABC = 360°
84° + 2∠ABD = 360° [∵ ∠ABD = ∠ABC]
2∠ABD = 276
∠ABD = 138°
Therefore, the measure of the angle ∠ABD is calculated as 138° from the given data and figure.
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The volume of a cube is 2744m^3. What is the length of an edge of the cube?
Answer:14
Step-by-step explanation
The answer is PROBABLY a whole number.
(2) 10^3 = 1000; 20^3 = 8000. So the number is between 10 and 20; and closer to 10.
(3) Of the possible answers 11, 12, 13, and 14, only one of them has units digit 4 when raised to the 3rd power.
Answer:
L=14m
Step-by-step explanation:
volume of a cube =L×L×L
V=L³
2744=L³
L=³√2744
L=14m
50 POINTS PLEASE SHOW WORK!!!! A radio telescope has a parabolic dish. Radio signals are collected at the focal point (focus) of the parabola. The distance from the vertex of the parabolic dish to the focus is 20 feet. The vertex of the dish is located at a point 30 feet above the ground and 80 feet to the east of a computer that reads and records data from the telescope. The diameter of the dish is 120 feet.
What is the depth of the parabolic dish?
In this exercise we have to use the knowledge of depth to be able to calculate the depth that is being seen by the telescope, in this way we can say that:
45 feet deep
First, knowing that the formula for the parabola is:
4py=x²
Now P is the distance from the vertex to the focus or to the directrix which is equal to 20, we can say that:
4(20)y=x²
80y=x²
Now we just should use individual knwon financial worth of X fashionable the maximum point of the dish, exist the measurement across object of the eating receptacle exist 120 extremities that is to say the maximum x, and we understand information that 120 extremities is heavy distance middle from two points the expansive -x and x, so those hopeful: -60 and 60.
80y=x²
80y=60²
80y=3600
y=45
Answer:
75ft
Step-by-step explanation:
We can let the parabola open upward......so we will have the form
4a ( y - k) = (x - h)^2
The distance from the vertex to the focus = 20 = a
We can let the vertex be ( 80, 30)
So we have the form
4(20) ( y- 30) = (x - 80)^2 simplify
80 ( y - 30) = ( x - 80)^2
Since the diameter is 120 ft...the radius is 60 ft.....so we can let one point on the parabola be ( 80 + 60 , a) =
(140 , a)......where a is the height of the dish....so we have that
80 ( a - 30) = (140 - 80)^2
80 ( a - 30) = (60)^2
80 ( a - 30) = 3600 divide both sides by 80
a - 30 = 45 add 30 to both sides
a = 75 ft = the height of the dish
Mario received $0.40 in change from
$20.00 when he bought trail mix. How
many pounds of trail mix did Mario buy?
please help me please
There is no question, just some graphs, I can not explain if I don't know the question
ok
y = 2x
This is a positive line that increases from left to right, because the number 2 of the equation is positive.
So from the graphs that you send me, the right answer is the second one, it is an increasing line.
A graph increases from left to rigth if it goes up
A graph decreases from left to right if it goes down
3. Solve the expression when a= 0.25 and b = -1
36a + 42b - 18a + 6
Answer:
-31.5
Step-by-step explanation:
36(0.25)+ 42(-1)-18(0.25)+6
9-42-4.5+6
=-31.5
how fast is soil creep? group of answer choices 1 to 10 millimeters per year 1 to 10 meters per year 1 kilometer per hour over 10 kilometers per hour
The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.
Given that,
In the picture we can see the options.
We have to select the correct option for the given question.
What is the soil creep?The slow, downward movement of rock and soil down a low grade slope is known as downhill creep, sometimes referred to as soil creep or simply creep. Downhill creep can also refer to the slow deformation of such materials as a result of persistent strain and tension. While creep may appear continuous to the spectator, it actually represents the accumulation of multiple little, discontinuous movements of slope material produced by gravity.
Therefore, The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.
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what is this???????????????????????/
Answer:
5rs^3t^2 cubed root rt
Step-by-step explanation:
so 5rs-cubed t-squared and inside the cube root is rt
The width of a rectangle measures (7r - 2s) centimeters, and its length measures
(r-5s) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
The perimeter of the given rectangle is 16r-14s centimeters.
Let width be represented by=w
Let length be represented by=l
Let perimeter be represented by=p
Then,
l=(r-5s)centimeters (Given in the question)
while w=(7r-2s)centimeters (Given in the question)
The formula for the perimeter of a rectangle= 2(l+b)
where l is the length while b is the breadth of the rectangle.
On putting values in the equation:
p=2(l+b)
p=2(l+w)
p=2[(7r-2s)+(r-5s)]
on opening the bracket 2 is multiplied by both terms.
p=2(7r-2s)+2(r-5s)
p=(2x7r-2x2s)+(2xr-2x5s)
p=(14r-4s)+(2r-10s)
p=14r-4s+2r-10s
p=14r+2r-4s-10s
p=14r+2r-(4s+10s)
p=14r+2r-(14s)
p=16r-(14s)
Thus,
p=16r-14s centimeters
The perimeter of the given rectangle is 16r-14s centimeters.
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5multipled 10the power 5 multipiled 4 multipled 10 to the power 3 divided by 2 multipled by 10 to the power minus 3
Step-by-step explanation:
answer
Are you clear your doubt with my answer?
Given H = f(t) where H is the height in meters of an object and t is the time in
seconds since it was launched, which of the following is the best interpretation of f(2) =18?
A. The object travels 2 meters for every 18 seconds.
B. 18 seconds after the object is launched it is traveling 2 meters per second.
C. The object is 36 meters in the air.
D. 2 seconds after the object is launched it is 18 meters in the air.
E. The object travels 18 meters for every 2 seconds.
F. 2 seconds after the object is launched it is traveling 18 meters per second.
G. 18 seconds after the object is launch it is 2 meters in the air.
Answer:
D
Step-by-step explanation:
Well, since t = time in air, we already know that it traveled 2 seconds.
H = height in meters, and H = 18
So, after 2 seconds the object is 18m in the air
So, option D
Interior and exterior angles
The measures of the interior and exterior angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠7, ∠8, and ∠9 are 90°, 90°, 90°, 122°, 58°, 58°, 148°, 32°, and 148°, respectively.
We are given a triangle. One of the angles is 122 degrees, as shown in the diagram. We need to find all the interior and exterior angles. The vertically opposite angles are equal. The angle ∠4 is vertically opposite to the given angle. So, ∠4 = 122°. The angle ∠5 and the given angle form a linear pair. So, the angle ∠5 = 180° - 122° = 58°. The angle ∠6 is vertically opposite to the angle ∠5. So, the angle ∠6 = 58°. The angles ∠1, ∠2, and ∠3 are angles made by coordinate axes that are perpendicular to each other. So, the angles ∠1 = ∠2 = ∠3 = 90°. Now we use the angle sum property of a triangle. The sum of all the interior angles of a triangle is 180°. So, we can write the equation : ∠6 + ∠1 + ∠8 = 180°. So, ∠8 = 180° - (∠6 + ∠1) = 180° - (58° + 90°) = 180° - 148° = 32°. The angles ∠8 and ∠9 form a linear pair. So, ∠9 = 180 - 32° = 148°. The angle ∠7 is vertically opposite to the angle ∠9. So, the angle ∠7 = 148°.
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The perimeter of a square is 44 centimeters. What is its area in square centimeters?
Answer:
121cm^2
Step-by-step explanation:
44/4=11 so each side equals 11cm
to find the area multiply height by width
11*11=121
121cm^2
URGENT WILL GIVE BRAINLIEST! NEED THIS ANSWER ASAP + 100 PTS.
A neighborhood is trying to set up school carpools, but they need to determine the number of students who need to travel to the elementary school (ages 5-10), the middle school (ages 11-13), and the high school (ages 14-18). A histogram summarizes their findings: Which of the following data sets is represented in the histogram?
{6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 2, 2}
{11, 11, 12, 5, 10, 7, 10, 8, 6, 11, 11, 12, 18, 14, 13}
{6, 5, 10, 12, 11, 7, 2, 14, 18}
{6, 14, 6, 8, 8, 19, 11, 12, 13, 10, 4}
Answer:
Step-by-step explanation:
The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram,the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}To learn more about histograms, please check: brainly.com/question/13053780
Find the coordinate of the given point.
The point Y between X(1,-2) and Z(11, 3) such that the ratio of XY to YZ is 3:2
[tex]\textit{internal division of a line segment using ratios} \\\\\\ X(1,-2)\qquad Z(11,3)\qquad \qquad \stackrel{\textit{ratio from X to Z}}{3:2} \\\\\\ \cfrac{X\underline{Y}}{\underline{Y} Z} = \cfrac{3}{2}\implies \cfrac{X}{Z} = \cfrac{3}{2}\implies 2X=3Z\implies 2(1,-2)=3(11,3)[/tex]
[tex](\stackrel{x}{2}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{33}~~,~~ \stackrel{y}{9}) \implies Y=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{2 +33}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4 +9}}{3+2} \right)} \\\\\\ Y=\left( \cfrac{ 35 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} Y=(7~~,~~1) \end{array}}[/tex]