We are given the following points:
[tex](0,-1);(0,-11)[/tex]We can use the formula for the euclidean distance:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,-1) \\ (x_2,y_2)=(0,-11) \end{gathered}[/tex]Replacing the values:
[tex]d=\sqrt[]{(0-0)^2+(-11-(-1))^2}[/tex]Solving we get:
[tex]d=\sqrt[]{(-11+1)^2}[/tex]Solving the square root
[tex]d=-11+1=10[/tex]Therefore, the distance is 10.
Jerome is constructing a table of values that satisfies the definition of a function.
It is important to know that a function associates to every elemento of x a unique element of y. In other words, x-values should no repeat. Having said that, we can't fill the blank with -1, 0, 11, or 17.
Hence, the answers are -5 and 2.f(x) = 3x - 3, find f (-4)
Answer:here x=-4
Step-by-step explanation:
3(-4)-3=-15
100 points and brainly for right answer A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
Answer:
y = 1/3x + 7
Step-by-step explanation:
A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
slope = change in rise/change in run
so:
slope = change in y/change in x
you are given two points in (x , y) format, points are: (9,10) and (6,9) [second in each pair are the y values]. Figure change in y and x:
y: 10 - 9 = 1
x: 9 - 6 = 3
so slope =y/x = 1/3
slope intercept form is: y = mx + b where m = slope. Substitute in value previously found for slope:
y = 1/3x + b
Now, you need to find y intercept, or b. Using one of the points given, we will use the first one (9,10), calculate for b:
y = 1/3x + b
10 = 1/3(9) + b
10 = 3 + b
subtract 3 from both sides:
10 - 3 = 3 + b - 3
b = 7
Put this into your equation: y = mx + b
y = 1/3x + 7
when Angel left his house in the morning his cell phone battery was partially charged. Let B represent the charge remaining and Angels battery, as a percentage, T hours since Angel left his house. A graph of B is shown below. Write an equation for fee then State the slope of the graph and determine its interpretation in the context of the problem
An international company has 29,200 employees in one country. If this represents 31.7% of the company's employees, how many employees does it have in total?Round your answer to the nearest whole number.
Answer:
The total number of employees the company have is;
[tex]92,114[/tex]Explanation:
Given that an international company has 29,200 employees in one country.
If this represents 31.7% of the company's employees.
let n represent the total number of employees the company have;
[tex]31.7\text{\% of n = 29,200}[/tex]Solving for n;
[tex]\begin{gathered} \frac{31.7}{100}n=29,200 \\ 0.317n=29,200 \\ n=\frac{29,200}{0.317} \\ n=92,113.564668 \\ n\approx92,114 \end{gathered}[/tex]Therefore, the total number of employees the company have is;
[tex]92,114[/tex]Establish the identity.
(sec 0+1)(sec 0-1)= tan 0
Multiply and write the left side expression as the difference of two squares.
- Tan²θ is the left side expression as the difference of two squares in trigonometric ratios.
What do trigonometric ratios represent?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. Trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios.When calculating unknown distances from known or measured angles in geometric figures, trigonometric functions are used.(sec θ+1)(sec θ-1)= tan² θ
use ( a+ b ) ( a - b) = a² - b²
= 1² - sec²θ { we know that 1 + tan²θ = sec²θ}
= 1 - sec²θ
= - tan²θ
LHS = RHS
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how do I graph r=6+3sintheta ?
Given:
[tex]r=6+3\sin \theta[/tex]Let's graph the equation.
Apply the formula:
[tex]r=a\pm b\sin \theta[/tex]Where:
a = 6
b = 3
Thus, we have the following:
Subsitute -θ for θ to know thw axis of symmetry:
[tex]\begin{gathered} r=6+3\sin (-\theta) \\ \end{gathered}[/tex]Now, solve for θ = 1 and -1:
[tex]\begin{gathered} r=6+3\sin (1) \\ r=6.05 \\ \\ r=6+3\sin (\text{ -1)} \\ r=5.94 \end{gathered}[/tex]Since sinθ is not equal to sin(-θ), the pole will be the point of symmetry.
To find the x-intercept, substitute 0 for θ:
[tex]\begin{gathered} r=6+3\sin \theta \\ \\ r=6 \end{gathered}[/tex]Hence, the limacon will cross the x-axis on both sides at x = 6 and -6.
Since the addition is with the sine function, the limacon will face down.
Now, input different values for θ and solve for r.
We have:
When θ = pi/2:
[tex]r=6+3\sin (\frac{\pi}{2})=9[/tex]When θ = pi:
[tex]r=6+3\sin (\pi)=6[/tex]When θ = 9pi/6:
[tex]r=6+3\sin (\frac{9\pi}{6})=3[/tex]Thus, we have the points:
[tex](\frac{\pi}{2},9),(\pi,6),(\frac{9\pi}{6},3)[/tex]Using the coordinates we have the graph:
John's utility bills for the last five months are $23.84, $23.87, $20.48, $29.75, and $28.34. Find John's mean utility bill over this period.
Answer:
[tex]\text{ \$25.26}[/tex]Explanation:
Here, we want to get the mean utilit bill over the period
Mathematically, that means we have to find the average of his utility bills in that period
To get this,we have to divide the sum of all these values by the count of these values (5)
Mathematically, we have this as:
[tex]\frac{23.84\text{ + 23.87 +20.48 + 29.75 + 28.34}}{5}=\text{ }\frac{126.28}{5}\text{ = \$25.26}[/tex]2. The hypothetical market for flu shots is depicted in the graph below where market equilibrium quantity is 20 flu shots and market equilibrium price is $20 per shot. Assume that there was an external benefit of $20 per flu shot (value of the flu shot by an individual that accrues to bystanders). What would be the socially optimal quantity of flu shots considering the effect of this external benefit? Answer = ____ flu shots How much of a subsidy per shot would make the market equilibrium outcome be equal to the socially optimal equilibrium? Answer = $____ per flu shot (/2.0 Points)
The socially ideal dose of 40 flu vaccines may be determined by the external beneficial effect. While a $10 subsidy for each flu shot would bring the market equilibrium's result into line with the ideal situation for society.
In order to determine customer interest in and market demands for products that are currently in development, hypothetical scenario marketing uses product surveys and made-up scenarios. Utilizing hypothetical marketing can assist small business owners in allocating resources to product categories where customers have shown a need and desire.
The presented example is a positive externality situation since there is an external social benefit and the market equilibrium quantity is lower than the level of output that would be considered optimal for society because it ignores the external benefit. The subsidy is applied to either produce internalities or address externalities per unit.
At each level, there will be a $20 rightward shift in the marginal social benefit curve. With this external benefit effect in mind, 40 shots of the flu vaccine would be the most beneficial for society. The market equilibrium result would be identical to the socially ideal equilibrium with a $10 subsidy for each flu vaccine.
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graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to c is 4/5. in other words a change of 1 unit in x corresponds to a change of 4/5 units in y
The graph that represents the proportional relationship between x and y with a unit rate of 4/5 is shown in the image below.
How to Graph the Line of a Proportional Relationship?If the relationship between x and y is a proportional relationship, the equation that models the relationship between x and y can be expressed as y = mx. Here, the unit rate is represented by the value of in the equation.
This means that, the graph that represents the proportional relationship between x and y would have a slope of the value of m. m, which is the slope of the line, is the ratio of the rose of the line to the run of the line.
Thus, where m = 4/5, the equation that represents the proportional relationship would be:
y = 4/5x.
Therefore, the graph below shows the proportional relationship between x and y which is represented by the equation, y = 4/5x.
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Graph the system of equations 2y=8x+18 24+4y=x
Answer:
draw the graphic vertical and edges line
put the dot on line
And put the 2y=8×+18 24+4y=×
Help DUE by 10:00 pm help
A regular polygon is shown.
15 sided regular polygon
Determine the measure of one of its angles.
156°
168°
2,340°
2,700°
The measure of the given polygon's angle is 2340°
Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.
In an n-sided polygon, there are n inner angles.
The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.
the formula is ;
Sₙ = ( n - 2 ) 180°
Here in question n is given as 15
Thus Sₙ = ( n - 2 ) 180° becomes
Sₙ = ( 15 - 2) 180
13 × 180
= 2340 °
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32 oz for 3.29 or 24 oz for 2.59 find the better buy round to the nearest cent or hundreth.
Determine the unit price of 32 oz for $3.29.
[tex]\begin{gathered} \frac{3.29}{32}=0.1028 \\ \approx0.10 \end{gathered}[/tex]Determine the unit price for 24 oz for $2.59.
[tex]\begin{gathered} \frac{2.59}{24}=0.1079 \\ \approx0.11 \end{gathered}[/tex]The unit price of 32 oz for $3.29 is less. So the better buy round is 32 oz for $3.29.
Divide. Reduce your answers to lowest terms.5/8 divide (-3 3/4)
Given data
5/8 divided by (-3 3/4)
Firstly, convert the mixed fraction into an improper fraction
[tex]\begin{gathered} -3\text{ }\frac{3}{4}\text{ can be converted to the below improper fraction} \\ -3\text{ }\frac{3}{4}\text{ = -}\frac{(4\text{ x (3) + 3}}{4} \\ -\text{ 3}\frac{3}{4}\text{ = - }\frac{12\text{ + 3}}{4} \\ -\text{ 3 }\frac{3}{4}\text{ = - }\frac{15}{4} \\ \text{Therefore, 5/8 divided by - 15/4} \\ \frac{5}{8}\text{ / -}\frac{15}{4} \\ \frac{5}{8}\text{ x -}\frac{4}{15} \\ =\text{ }\frac{-20}{120} \\ =\text{ - }\frac{1}{6} \end{gathered}[/tex]Answer = - 1/6
5) Determine the probability distribution's missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
For the given probability distribution, the missing value is 5/17.
What is probability distribution?A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.
For the given distribution,
Let the missing value be x
we know that sum of probabilities = 1
⇒ 0 + 0 + 7/17 + x + 5/17 = 1
⇒ 12 / 17 + x = 1
⇒ x = 1 - 12/17
⇒ x = 5 / 17
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Order the following functions by growth rate
The following functions have the following growth rates:
2/N < 37 <√N < N < N log log N < N log N < N log(N^2) < N . log^2 . N < N^1.5 < N^2 <N^2. log N < N^3 < 2^N/2 < 2^N
How can you determine a function's growth rate?
The present value is divided by the past value, multiplied to the 1/N power, and then one is subtracted to get the formula for the average growth rate over time approach.
How may the growth rates of two functions be compared?
Determine the limit limxf(x)g(x) lim x f (x) g (x) given the functions f(x) and g(x).The growth rate of f(x) is a times the growth rate of g(x) for sufficiently large x if the limit in Step 1 is a finite constant a0 a 0.To learn more about functions click on the link below:
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Use the drawing tool(s) to form the correct answer on the provided graph.
The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2 f (x - 1)
ights reserved
Drawing Tools
Select
Line
Click on a tool to begin drawing
-8
-6 4
Undo
Reset
The finished graph of g(x) = 2f(x - 1) would be as seen in red.
What is defined by the term transformation?Image transformations usually involve the modification of various bands of data, either from a single source images or from two or more images acquired at different times of the same area.We were provided a graph of the function f(x).
g(x) = 2f is another function definition (x -1).
Now we must use the drawing tool(s) to create the proper graph of a function g(x) = 2f (x -1).
which can be discovered through transformation.
f(x) becomes f (x-1)
Then, f(x-1) becomes 2f (x-1)
f(x-1) shifts this same graph of f(x) by one unit to the right.
Whereas 2f(x-1) extends the graph of f(x-1) by a factor of 2. So we just need to double the y-coordinates of the points on the graph.
As a result, the finished graph of g(x) would be as seen in red.
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PLEASE HELP!!!!!
Answer two questions about Equations AAA and BBB:
A. x/4 + 1 = -3
B. x + 4 = -12
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
(Choice A)
Rewrite one side (or both) using the distributive property
(Choice B)
Rewrite one side (or both) by combining like terms
(Choice C)
Multiply/divide only one side by a non-zero constant
(Choice D)
Multiply/divide both sides by the same non-zero constant
Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
(Choice A)
Yes
(Choice B)
No
Answer:
1)D and 2)A
Step-by-step explanation:
1) D
When you dived B by 4 on both sides , you get A
2) A
:]
Jen purchased the items shown in the table.
Item Cost ($)
shirt 11.99
shoes 35.50
belt 6.75
socks 3.00
In the city she lives in, the sales tax rate is 7.15%. In another city, the sales tax rate is 6.35%. How much more is she spending if she purchases the items in the city where she lives? Round to the nearest cent.
She spends the cost of $0.46 if she purchases the items in the city where she lives.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given data below as:
Cost of the shirt = $11.99
Cost of the shoes = $35.50
Cost of the belt = $6.75
Cost of the socks = $3.00
Total cost of the items = 11.99 + 35.50 + 6.75 + 3.00
Total cost of the items = $57.24
In the city she lives in, the sales tax rate is 7.15%.
Total cost of the items with tax of 7.15%
= 57.24 × 7.15/100 + 57.24 = 4.092 + 57.24 = $61.33
In another city, the sales tax rate is 6.35%
Total cost of the items with tax of 6.35%
= 57.24 × 6.35/100 + 57.24 = 3.633+ 57.24 = $60.87
Hence, she spends the cost of $0.46 if she purchases the items in the city where she lives.
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Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 12 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 8740 dollars. How much did she invest at each rate?Amount invested at 4 percent interest is $Amount invested at 12 percent interest is $
We will have the following:
First, we recall that the simple interest formula is given by:
[tex]A=P(1+rt)[/tex]Now, for the accounts that are described in the problem we will have that:
[tex]\begin{gathered} A_1+2P=2P(1+(0.04)(1))\Rightarrow A_1+2P=2P(1.04) \\ \\ A_2+P=P(1+(0.12)(1))\Rightarrow A_2+P=P(1.12) \end{gathered}[/tex]Now, we have that:
[tex]A_1+A_2=8740[/tex]Then:
[tex]\begin{gathered} A_1+A_2+2P+P=2P(1.04)+P(1.12) \\ \\ \Rightarrow8740+3P=3.2P\Rightarrow8740=0.2P \\ \\ \Rightarrow P=43710 \end{gathered}[/tex]So, the amount invested at 4% interest is $87 420.
And, the amount invested at 12% interest is $43 710.
the ratio to use to find the area of the sector is ____.the area of the circle is ____. the area of the sector is ____.
Ratio = 1/6
Area of circle = 64π
Area of sector = 64π/6 = 32π
Explanation:Area of sector when measured in degrees:
[tex]Areaof\sec tor\text{ = }\frac{\theta}{360}\times\pi r^2[/tex]The ratio here is the ratio of the central angle to 360
ratio = 60/360 = 1/6
the ratio to use to find the area of the sector is 1/6
Area of a circle = πr²
r = radius = 8
Area of a circle = π × 8² = π × 8 × 8
Area of the circle = 64π
Area of sector:
θ = 60°
Area of sector when measured in degrees:
[tex]Areaof\sec tor\text{ = }\frac{\theta}{360}\times\pi r^2[/tex][tex]\begin{gathered} =\frac{60}{360}\times\pi\times8^2 \\ =\frac{1}{6}\times\pi\times8^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of sector = }\frac{64}{6}\pi\text{ (in simplest form)} \\ \text{Area of sector = }\frac{64}{6}\pi\text{ = }\frac{32}{3}\pi \end{gathered}[/tex]What is the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}?
O {1, 2, 3, 4)
O {2, 4, 6}
O (2, 4)
O {1, 2, 3, 4, 6}
Answer:
(b) {2, 4, 6}
Step-by-step explanation:
You want the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}.
RangeThe range of a relation is the set of possible output values. When values are listed as ordered pairs, it is the set of second numbers of those pairs.
The list of second numbers is ...
2, 4, 2, 6
When these are expressed as a set, duplicates are removed, and they are listed in order:
{2, 4, 6} . . . . the range of the relation
Which triangle is similar to △JKH?
1. △MKN
2. △JOG
3. △MQL
4. All triangles are similar to △JKH
Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN
What are similar triangles in geometry?Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.
The given parameter is Line a is parallel to Line b, which gives: a║b
Two triangles are similar if they satisfy the following conditions:
Two angles in one triangle are equal to two angles in the other triangle.Each of the three corresponding sides of the two triangles are proportional.Two sides of one triangle are proportional to the corresponding two sides on the other triangle, and the included angle between the specified two sides in both triangles are congruent.According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN
Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN
Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.
The correct option for the triangle similar to ΔJKH is option 1. ΔMKN
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Toni is at a dock on a bank of a straight river that is 1 mile wide and wants toreach the barge toll gate on the other side, so he can warn the guards about the stolengoods on an approaching barge. The toll gate is 4 miles downstream on the opposite bank,and Toni want to get there by first rowing his boat to somewhere (call it point P) on theopposite bank and then walking the remaining distance × to the toll gate. He can row at 4mph and walk at 2 mph. Express the total time 7, in terms of x, that he takes to go from thedock to the toll gate.
The formula to calculate the time taken is given to be:
[tex]Time=\frac{Distance}{Speed}[/tex]The total time taken is going to be the sum of the time taken to cross the river and the time taken to go from the point on the opposite bank to the toll gate.
The
Find the scale factor of APMN to AZXY. * X 4 b Z 6 10 9 NV
Answer:
The scale factor is 5 / 2
Explanation:
The scale factor is the ratio of the side lengths of the bigger triangle to the smaller triangle.
The scale factor is also the ratio of the corresponding sides of the two traingles.
The ratio of MP to XZ is
[tex]\frac{MP}{XZ}=\frac{10}{4}[/tex]Simplification gives
[tex]\frac{5}{2}[/tex]Hence, the scale factor is 5 /2 or 2.5.
If 5 friends want to share 1.25 of a pizza evenly how much pizza would each person get?
Answer:
0.25
Step-by-step explanation:
1.25 ÷ 5 = 0.25
Answer = 0.25
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Which equation represents a proportional relationship A y=3x/4B y=3/4x C y=3x/4 +1D y=3/4x +1
Answer: Out of the given options, we need to pick a relationship that is proportional:
In general, an equation that represents a proportional relationship has the following form:
[tex]y=kx[/tex]Therefore, the following is a proportional equation:
Option-(A)
[tex]\begin{gathered} y(x)=\frac{3}{4}x \\ k=\frac{3}{4} \end{gathered}[/tex]Explanation:
Because there is a constant multiple or a coefficient, and it indeed matches the form of equations that are proportional.
Find the value of p if the sum of negative 4
and the quantity p divided 5 is sixteen.
A. 4
B. -60
C. 60
D. 100
Answer:
100
Step-by-step explanation:
[tex] - 4 + \frac{p}{5} = 16[/tex]
Multiply through by the LCM which is 5
[tex] 5 \times \frac{ - 4}{1} + 5 \times \frac{p}{5} = \frac{16}{1} \times 5[/tex]
[tex] - 20 + p = 80[/tex]
[tex]p = 80 + 20[/tex]
[tex]p = 100[/tex]
A person 1.85 m tall walks towards a lamppost on level ground at a rate of 0.5 m/sec. The lamp on the post is 5 m high. At which rate is the tip of the person's shadow moving toward the lamppost when the person is 4 I from the post? Please enter your answer in decimal format with three decimal places.
Using the Pythagorean Theorem and implicit differentiation, it is found that the tip of the person's shadow is moving toward the post at a rate of 0.393 m/sec when the person is 4 m from the post.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom that relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, we have that:
The distance d between the person's shadow and the lamp is the hypotenuse of a right triangle.The legs are the person shadow and the lamp.Hence the following relation between these variables is established:
d² = x² + y².
Applying implicit differentiation, the rate of change of the distance is given as follows:
[tex]d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The height remains constant, hence:
[tex]\frac{dy}{dt} = 0[/tex]
The other parameters are given as follows:
y = 5 - 1.85 = 3.15 m (vertical distance).x = 4 m (distance of the person from the post).dx/dt = 0.5 m/s (velocity of the person).Hence the distance at the desired instant is:
d² = 4² + 3.15²
d = sqrt(4² + 3.15²)
d = 5.091 m
The rate of change of the distance is found as follows:
5.091dd/dt = 4 x 0.5
dd/dt = 2/5.091
dd/dt = 0.393 m/sec.
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The x-intercept of 2x + 3y = 12 is (0,4).A.TrueB.False
The x intercept is the value of x when y = 0
Looking at the equation,
2x + 3y = 12
If we substitute y = 0 into the equation, it becomes
2x + 3*0 = 12
2x + 0 = 12
2x = 12
x = 12/2
x = 6
Therefore, the statement is false