Determine the continuity at x = 2. Be sure to clearly state your reasoning. fastest answer get ranked brainliest
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The answer is in my screenshot pic.
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HELP I DONT UNDERSTAND THEIS QUESTIIONS
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1) f(x)-3
[tex]\begin{gathered} f(x)=2x-4 \\ \Rightarrow f(x)-3=2x-4-3 \end{gathered}[/tex]Therefore, f(x)-3=2x-4-3
2) f(x-3)
[tex]\Rightarrow f(x-3)=2(x-3)-4[/tex]Thus, f(x-3)=2(x-3)-4
3) f(-3x)
[tex]f(-3x)=2(-3x)-4[/tex]Then, f(-3x)=2(-3x)-4
4) -3f(x)
[tex]-3f(x)=-3(2x-4)[/tex]Hence, -3f(x)=-3(2x-4)
Carolyn leases a new Hyundai Elantra by paying $2600 up front and $170 a month over three years. The lease also stipulates he will be charged $0.12 per mile for every mile over 36,000. If she puts 40,693 miles on the car, what will be the total cost of the lease?
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4,693 x $0.12= $563.16 (cost of the mile overage)
3 years= 36 months. (Multiply 3 x 12)
Now multiply 36 x $170 a month = $6,120.
$2,600 (up front cost) + $563.16 (cost of mile overage) + $6,120 (cost over 3 years) = $9.283.16 ( answer)
Which graph shows a proportional relationship between the number of hours of renting a pair of roller skates and the total amount spent to
rent the roller skates?
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Answer:
You were right. The answer is (C)
Step-by-step explanation:
Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.
RCX)=2VX SCx) = x(RSX4=
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Given the two functions:
[tex]\begin{gathered} R(x)=2\sqrt[]{x} \\ S(x)=\sqrt[]{x} \end{gathered}[/tex]We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:
[tex](RoS)(x)=2\sqrt[]{\sqrt[]{x}}[/tex]When we plug in "4", into "x", we have:
[tex]\begin{gathered} (RoS)(x)=2\sqrt[]{\sqrt[]{x}} \\ (RoS)(4)=2\sqrt[]{\sqrt[]{4}} \\ =2\sqrt[]{2} \end{gathered}[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
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The correct option is True, there is enough information given to say that both line are parallel.
What is termed as as the supplement angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.For the given question.
The two lines are given with angles measure from 1 to 8.
Where,
∠4 = 89°∠3 = 91°As, the sum of the angles is;
∠4 + ∠3 = 91° + 89°
∠4 + ∠3 = 180° (supplementary angles)
Thus, we can say that both lines are parallel to each other.
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Find the constant of proportionality for the proportional relationship between weight and cost shown in the table. Then find the cost of 10 oz of green beans. Cost of Green Beans Weight (oz) Cost($) 8 1.12 12 1.68 16 2.24 The constant of proportionality is $0.14 per ounce. The cost of 10 oz of green beans is $ VE S 4.1 More 10 Enter your answer in each of the answer boxes. Next Back of 16 Question 1 Review progress
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What is the answer pleasee
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The value of interior angle x for the given pentagon if found as 88 degrees.
What is termed as the pentagon?A pentagon is a two-dimensional polygon with 5 sides and 5 angles.This shape should have five sides and form a closed two-dimensional figure. A closed figure consists of each of its sides intersecting to form vertices.Five diagonals connect the five vertices to one‘s opposite vertices in a pentagon shape.Each interior angle in a regular pentagon is 108°, so each exterior angle is 72°.For the given question;
The exterior angles of the pentagon are given in figure.
Find all the interior angles for given angles using linear pair as all are straight lines.
180 - 62 = 118180 - 33 = 147180 - 114 = 66180 - 59 = 121The sum of all the interior angle of pentagon is 540.
Thus,
118 + 147 + 66 + 121 + x = 540
x = 540 - 452
x = 88
Thus, the value of interior angle x for the given pentagon if found as 88 degrees.
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Select the reason why these triangles are similar. If they are not, select "Not similar". 88 3 2 88 B. SAS A. AA D. Not similar C. SSS
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From the given figure
The 2 triangles have one equal angle of measure 88
The side of length 3 and the side of length 1 have a ratio 3: 1
The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1
That means we have one equal angle and two proportional sides
Since the angle is between the proportional sides, then
The 2 triangles are similar by the SAS postulate
Answer B
Does anyone understand this geometry question
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Answer:
This is an isosceles right triangle, so
x = 45°.
Given f(x) = ln(x), which is the correct answers ?
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First, lets perform each transformation and then take a look at its graph:
1.
[tex]\begin{gathered} g(x)=-\frac{1}{2}f(x-2) \\ \\ \Rightarrow g(x)=-\frac{1}{2}\ln (x-2) \end{gathered}[/tex]The only etiquette that matches this plot is: Function decreases as x increases
2.
[tex]\begin{gathered} h(x)=f(x-\frac{1}{2}) \\ \\ \Rightarrow h(x)=\ln (x-\frac{1}{2}) \end{gathered}[/tex]The only etiquette that matches this plot is: x-intercept at (1.5 , 0)
3.
[tex]\begin{gathered} j(x)=f(x)-\frac{1}{2} \\ \\ \Rightarrow j(x)=\ln (x)-\frac{1}{2} \end{gathered}[/tex]The only etiquette that matches this plot is: Asymptote of x = 0
Stanley bought sneakers, a pair of pants, a t-shirt and a jacket for $535.00. The sneakers cost 5 less than the jacket, the pants cost $50 less than the jacket, and the t-shirt cost $10 less than three times the jacket. Find the cost of each item.
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The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.
This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.
The cost of all the items is equal to $535
s + p + j + t = $535 ......(1)
Sneakers cost $5 less than the jacket
s = j - $5 ......(2)
Pants cost $50 less than the jacket
p = j - $50 ......(3)
T-shirt cost $10 less than three times the jacket
t = 3j - $10 ......(4)
Putting the values of equation (2), (3) and (4) in equation (1)
j - $5 + j - $50 + j + 3j - $10 = $535
6j = $535 + $65
=> 6j = $600
=> j = $100 which is the cost Jacket.
Now, s = $100 - $5 = $95 which is the cost of Sneakers.
p = $100 - $50 = $50 which is the cost of pair of pants.
t = $300 - $10 = $290 which is the cost of t-shirt.
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Find the area of this circle.Use 3.14 to approximate n.Α = πη28 inA = [ ? ] in?
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To find the area of a circle given its radius,
[tex]\text{Area}=\pi\times r^2[/tex]The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;
[tex]\begin{gathered} \text{Area}=3.14\times8^2 \\ \text{Area}=3.14\times64 \\ \text{Area}=200.96in^2 \end{gathered}[/tex]The area of the circle is 200.96 inches squared
Write the equation of the perpendicular bisector of XY if endpoint X is at (-9,1) and endpoint Y is at (3,5). A) y = -X B) y = 3x - 6 C) y = -3x - 6 D) y = 3x + 12
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A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.
First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows
[tex]\begin{gathered} M=(\frac{-9+3}{2},\frac{1+5}{2}) \\ M=(\frac{-6}{2},\frac{6}{2}) \\ M=(-3,3) \end{gathered}[/tex]This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-1}{3-(-9)}=\frac{4}{3+9}=\frac{4}{12} \\ m=\frac{1}{3} \end{gathered}[/tex]Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.
[tex]\begin{gathered} m_1\cdot m=-1 \\ m_1=\frac{-1}{m} \\ m_1=-\frac{1}{\frac{1}{3}}=-3 \end{gathered}[/tex]Now, we use the slope-point formula to find the equation for the perpendicular bisector.
[tex]y-y_1=m(x-x_1)[/tex]Where we replace the slope -3 and the point (-3,3).
[tex]\begin{gathered} y-3=-3(x-(-3)) \\ y-3=-3x-9 \\ y=-3x-9+3 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the right answer is C.MARKING BRAINLIEST What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
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The lengths of the major and minor axis of the ellipse, are; 4√6 and 4√3 respectively.
What is an ellipse in coordinate geometry?An ellipse describes the locus of a point on a curve, such that the sum of the distance between two focal points from the points on the curve is a constant.
The function of the ellipse can be calculated as follows;
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Where (h, k) = The coordinates of the center of the ellipse
a = The length of the semi-major axis
b = The length of the semi-minor axis
Now,
[tex]\dfrac{(x-3)^2}{12} + \dfrac{(y+ 4)^2}{24} =1[/tex]
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2√6
b = √(12) = 2√3
The length of the major axis is 2a
The length of the minor axis is 2b
The length of the major axis will be;
2a = 2 × 2√6 = 4√6
The length of the minor axis will be;
2b = 2 × 2√3 = 4√3
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Let's take a look at (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2). While Beeker believes that these two expressions are equal for all real numbers x and y Clod believes they are not! Let's get to the bottom of this!
a) Evaluate (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2) for x = 7 and y = 11
b) For which values of x and y does (x + y)^2 (x - y)^2 equal (x^2 + y^2)(x^2 - y^2)? For which values of x and y does (x + y)^2 (x - y)^2 not equal (x^2 + y^2)(x^2 - y^2)?
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From the given expression, it is found that:
a) When x = 7 and y = 11, the numeric values are given as follows:
(x + y)²(x - y)² = 5184.(x² + y²)(x² - y²) = 12240.b) They will only have the same numeric value when x = y.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.
The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.
In the context of this problem, the expressions are given as follows:
(x + y)²(x - y)².(x² + y²)(x² - y²).When x = 7 and y = 11, the numeric values are given as follows:
(11 + 7)²(11 - 7)² = 5184.(11² + 7²)(11² - 7²) = 12240.The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.
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Astronomers discover an exoplanet (a planet of a star other than the Sun) that has an orbital period of 3.95 Earth years in its circular orbit around its sun, which is a star with a measured mass of 3.97×1030kg . Find the radius of the exoplanet's orbit.
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The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.
How to calculate the radius of the exoplanet's orbit?In order to calculate the radius of the exoplanet's orbit, we would apply Kepler's Third Law of planetary motion.
Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:
T² = 2π√(r³/GM)
Where:
T represents the orbital period.M represents the mass.G represents the universal gravitational constant.r represents the radius.Making radius (r) the subject of formula, we have:
Radius, r = ∛(GMT²/2π)
Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².
Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds
Substituting the given parameters into the formula, we have;
Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)
Radius, r = 4.71 × 10¹¹ meters.
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What is the Expanded form of 45,803
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Answer: 40000
+ 5000
+ 800
+ 3
Step-by-step explanation:
The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
in the standard (x y) coordínate plane what’s the slope of a line that’s perpendicular to
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Answer:
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
One ounce is 28.35 grams. Convert16 ounces into grams. Round to nearest tenth
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16 ounces is equivalent to 453.6g when rounding to nearest tenth.
What is rounding off ?
Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.
To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.
here the given data is :
1 ounce = 28.35 grams
Conversion of ounce to grams :
This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.
The easiest way about this is simply multiply 16 by 28.25g
1 ounce = 28.35 grams
16 ounce = x
x = 16 x 28.25
x= 453.6 g
From the calculations above, 16 ounces is equivalent to 453.6g.
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I need help with this question but no one is helping me! Can someone please help me
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Answer:
the probability is 2/8
Step-by-step explanation:
This is my practice review me I have unlimited attempts. I need help with this question
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Let x represent the number of pounds of coffee that she bought.
From the information given,
cost per pound of coffee = $8.73
Cost of x pounds of coffee = 8.73 * x = 8.73x
Initial amount that she had = $90
After spencing $8.73x, the amount left is $63.81. This means that
90 - 8.73x = 63.81
8.73x = 90 - 63.81
8.73x = 26.19
x = 26.19/8.73
x = 3
She bought 3 pounds of coffee
Y=-3/2x-1. Graph integers?
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The graph of the figure is attached below.
Given equation of line:-
y = (-3/2)x - 1
First we will find the x and y intercepts of the line to plot in the line.
Putting x = 0 to find the y-intercept, we get,
y = (-3/2)(0) - 1
y = -1
Hence, the coordinates of the point are (0,-1).
Putting y = 0 to find the x-intercept, we get,
0 = (-3/2)x - 1
1 = (-3/2)x
x = -2/3
Hence, the coordinates of the point are (-2/3,0).
We can find another point on the line.
Putting x = 2, we get,
y = (-3/2)(2) - 1
y = -3 - 1
y = -4
Hence, the coordinates of the point are (2,-4).
Plotting these in a graph, we can get a straight line.
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What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
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Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]
Step-by-step explanation:
The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].
Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].
Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].
number in expended form
675,432
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Answer: 600,000 + 70,000 + 5,000 + 400 + 30 + 2
Explanation:
Each digit forms a different number depending on its place value.
The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well
are all angles are congruent to one another
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Answer:
Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
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1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.
2. The balance in Tammy's investment account at the end of last year was $7,585.
What is the percentage?The percentage is the proportion of a value in relation to another.
Percentages show how much a variable is contained in another.
The percentage gives the fractional value of the decrease in the investment account.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.
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radicals that have the same index and the same radicand is this true
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Given the expression;
[tex]\frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}[/tex]Step 1:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2} \\ \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} \sqrt[]{2}\times\sqrt[]{2}=2 \\ \sqrt[]{7}\times\sqrt[]{7}=7 \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2}=\frac{2\times7}{7} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=\frac{2\times7}{7} \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=2 \end{gathered}[/tex]The solution is;
[tex]2[/tex]Need help with a geometry problem. it is a scalene triangle with a parallel line through it which is x+1. the base is going to be 3x-2 and is parallel with x+1. on the right of x+1 there should be 12 at the top then 20 will split it . I need to solve for x
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A worker in an assembly line takes 7 hours to produce 31 parts. At that rate, how many parts can she produce in 28 hours?
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Answer:
124
Step-by-step explanation:
Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.
[tex]31(4)=124[/tex]
Factor 540 into product of prime factors
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Step 1
Given;
[tex]540[/tex]Required; To factor it out into products of prime factors.
Step 2
A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number is a prime factor. Examples of prime factors are; 1,2,3,5 etc. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.
Step 3
Find the prime factor of 540
Therefore, the prime pr