We checked the equation of lines are not parallel to each other.
What are parallel lines?
The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.
Two parallel lines never intersect.
Does the two lines parallel?equation of line passes through the point (- 3, -3) and (3, 9)
is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}
[ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]
(y +3) = [(9+3)/ (3+3)] (x+3)
y+ 3 = 12/ 6 (x+3)
y+3 = 2 (x+3)
y+3 = 2x+6
y = 2x+3 this is the first line.
equation of line passes through (-5, 12) and (1, 0)
[y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]
y -12 = -12/ 6 (x+5)
y - 12 = -2 x - 10
y = - 2x + 2
the above is the equation of second line.
the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.
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Identify the range of the function shown in the graph.
OA. -1 sy≤ 1
OB. {-1, 1)
OC. y> -1
-10
D. y is all numbers.
10
8
8-
2
48
-6
88
-10-
The range of the attached function is 0 ≤ y ≤ 8
How to determine the range?The complete question is added as an attachment
From the graph, we have the following highlights
Vertex = MaximumVertex = (0, 8)This means that the y value do not exceed 8, and the minimum is 0
Hence, the range of the attached function is 0 ≤ y ≤ 8
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Decide if the random variable x, is discrete or continious: x represents the temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
Answer:
Continuous
Step-by-step explanation:
Degrees don't always have to be integers. It can be 32.3 degrees, 32.31 degrees, etc.
17
The product of two positive numbers is
Calculate the numbers.
5/6
And their quotient is 15/8 calculate the number
Answer:
Let "x" and y" be the two numbers.
We have
xy = 5/6, (1) and x/y = 15/8. (2)
Multiply (1) and (2) (both sdes). You will get
x^2 = (5*15)/(6*8) = 25/16.
Hence, x = +/- 5/4.
Next, divide (1) by (2) (both sides). You will get
y^2 = 5/6:15/8 =
(5*8)/(6*15) = 4/9.
Hence, y=+/-2\/3.
Answer. There are two solutions: (x, y)=(5\/4,2\/3) and (x,y) = (-5/4,-2/3).
// We should exclude the second solution, since the numbers are negative.
Select all the true statements. Logarithms may be used to linearize data. Powers may be used to linearize data. Roots may be used to linearize data. If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model. If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
The true statements are:
Logarithms may be used to linearize data.
Powers may be used to linearize data. Roots may be used to linearize data.
If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model.
Another format for writing exponents is in logarithms.
The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Exponent and logarithm are inverse forms of one another. A logarithm is defined using an exponent.
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Answer:
A.Logarithms may be used to linearize data.
B.Powers may be used to linearize data.
C.Roots may be used to linearize data.
E.If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
Step-by-step explanation:
Yes
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule
The point estimate of the proportion of students who prefer the new schedule is 0.22.
Definition of Point Estimate
Point estimation is a technique used in statistics to determine a single value that will serve as the "best guess" or "best estimate" of an unidentified population characteristic, known as the point estimate. More precisely, in order to produce a point estimate, we apply a point estimator to the data.
For the confidence interval (0.195, 0.245), point estimate is calculated as follows,
p = (0.195 + 0.245) / 2
p = 0.44 / 2
p = 0.22
Hence, the point estimate of the proportion of students who prefer the new schedule comes out to be 2.2.
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What makes this graph misleading?
Different bar widths
The bars should be horizontal
Inconsistent scale on the y-axis - Correct
Y-axis didn't start at zero
The reason the graph given is misleading is that there is an Inconsistent scale on the y-axis.
Why is the graph misleading?The y-axis is inconsistent because it went from 0 to 200 and instead of continuing to increase by 200, it begins to increase by 10.
This is misleading because the scale used has to be uniform or else it would be hard to read the data.
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y is inversely proportional to x².
When x = 4, y = 2.
Find y when x = 1 divided by 2
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
y is inversely proportional to [tex]\sf{x^2}[/tex].✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏
If y=2 when x=4, what is y when x=[tex]\frac{1}{2}[/tex] ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex] ✏
If y is inversely proportional to x^2, the equation looks as shown below:-
[tex]\sf{\longmapsto{y=\cfrac{k}{x^2}}[/tex], where k -- constant of proportionality
Plug in all values
[tex]\sf{\longmapsto{2=\cfrac{k}{4^2}}[/tex] , simplifying --
[tex]\sf{\longmapsto{2=k/16}[/tex]
multiply by 16 both sides
[tex]\sf{\longmapsto 2*16=k}}[/tex]
[tex]\sf{\longmapsto{32=k}}[/tex]
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Plug 32 into the second equation:-
[tex]\sf{\longmapsto y=\cfrac{32}{\bigg(\cfrac{1}{2}\bigg)^2}}[/tex]
simplify the complex fraction
[tex]\longmapsto\sf{y=\cfrac{32}{\cfrac{1}{4}}[/tex]
divide fractions
[tex]\sf{\longmapsto{y=\cfrac{32}{1}\div\cfrac{1}{4}}=\cfrac{32}{1}\cdot}\cfrac{4}{1}}=128}[/tex]
`hope that was helpful to u ~
In the context of data models, relationships among records in a hierarchical model are called _____.
In the context of data models, relationships among records in a hierarchical model are called Branches. This is further explained below.
What are data models,?Generally, The act of generating a visual representation of either a whole information system or portions of it in order to express the linkages between different data points and structures is known as data modeling.
In conclusion, When discussing data models, the connections between different records in a hierarchical structure are referred to as "Branches."
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what is the maximum number of relative extrema contained in the graph of this function ? F(x) = 3x^4 - x^2 + 4x - 2
The maximum number of relative extrema of the given polynomial is; 3
How to find the maxima of a Polynomial Function?When trying to find the maximum number of relative extrema of a polynomial, we usually use the formula;
Maximum number of relative extrema contained in a polynomial = degree of this polynomial - 1.
We are given the Polynomial as;
f(x) = 3x⁴ - x² + 4x - 2
Now, the degree of the Polynomial would be 4. Thus;
Maximum number of relative extrema = 4 - 1
Maximum number of relative extrema = 3
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How many ways can seven finalists for a job be selected from eleven interviewees?
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been translated to produce figure 2.
Graph shows 2 quadrilaterals plotted on coordinate plane. Quadrilateral 1 in quadrant 2 has vertices at (minus 6, 3), (minus 5.5, 5), (minus 3.5, 5), (minus 3, 3). Quadrilateral 2 in quadrant 1 has vertices at (2, 1), (2.5, 3), (4.5, 3), (5, 1).
This translation can be described by
,
).
Answer:
A translation 8 units right and 2 units down
Kat plays a surfing video game with a friend. Each player earns 50 points for each trick he performs, but loses 40 points each time he falls off the surfboard. Last week, Kat had 6 stunts and 9 falls. Her score from her today was 3 times her score from last week. What was Kat's score today. What would be different about Kat's score today if it were –3 times her score from last week? What would be the same? Explain your reasoning.
Step-by-step explanation:
No. of points got from 1 stunt = 50.
No. of points deducted from 1 fail = 40.
6 stunts and 9 falls were gained last week.
So, A/C the number of points earned =
(6×50)-(9×40)
= 300 - 360
= -60
Her score today is 3 times her score from last week so multiply by 3
= (-60) × 3
= -180
If it were multiplied by -3 instead of 3 it would be...
(-60) × (-3)
= 180
The difference would be that on multiplying with positive 3 she would be 180 points in the whole but multiplying with negative three means she is 180 points in the league.
The similarity is that that whole number is same but the symbol adds a difference and the absolute value would be same too.
In a quadrilateral help he is congruent to lp what other condition would prove that help is a parallelogram
Answer: [tex]\overline{EL} \cong \overline{HP}[/tex]
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides is a parallelogram.
the angle 01 is located in quadrant iii, and cos(01) = -13/15. what is the value of sin (01)?
The value of sin(∝) is -√56/15
How to evaluate the sine angle?The given parameter is:
cos(∝) = -13/15
To determine the sine, we use the following identity
sin^2(∝) = 1 - cos^2(∝)
So, we have:
sin^2(∝) = 1 - (-13/15)^2
This gives
sin^2(∝) = 1 - 169/225
Evaluate the difference
sin^2(∝) = 56/225
Take the square root of both sides
sin(∝) = ±√56/15
sin(∝) is negative in quadrant III.
So, we have:
sin(∝) = -√56/15
Hence, the value of sin(∝) is -√56/15
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write an equation of a line perpendicular to y = 7 and passes through the point (3, -1).
Answer: x = 3
Step-by-step explanation:
The equation of the line perpendicular to a horizontal line is a vertical line, which has an equation of the form x=c.
the area of a rectangle is 344in²; if the length is 78in, find the width and perimeter of the rectangle
what is the width and perimeter
Most Swiss starlings produce four to five eggs in each clutch. Starlings producing fewer or more than this have reduced fitness. Which of the following terms best describes this situation
The term that describes the situation is called: stabilizing selection.
What is Stabilizing Selection?Unlike disruptive selection (diversifying selection) that tends to favor extreme traits when changes occur, stabilizing selection is defined as changes in population genetics in which extreme traits are not favored, rather, traits that are of intermediate variants are most favored and selected for.
Stabilizing selection can simply be described as the exact opposite of disruptive selection.
In the scenario given, traits of producing fewer starlings or more are extreme traits that are not favored and have reduced fitness. Intermediate variants of producing moderate number of starlings that have high fitness demonstrates the type of selection that is referred by the term called: stabilizing selection.
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2 (3/4 - x/3) = 1 1/4
solve for x
The value of x is 17/12
How to solve for x?The equation is given as
2 (3/4 - x/3) = 1 1/4
Express as improper fractions
2 (3/4 - x/3) = 5/4
Divide through by 2
3/4 - x/3 = 5/9
Collect like terms
x/3 = 3/4 - 5/9
Multiply through by 3
x = 9/4 - 15/9
Evaluate
x = (81 - 30)/36
Evaluate
x = 51/36
Simplify
x = 17/12
Hence, the value of x is 17/12
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simplify 16-4(3x-2)²
16-4(3x-2)²
=16-4(3x-2)(3x-2)
=16+−36x²+48x+−16
=(−36x²)+(48x)+(16+−16)
=−36x²+48x
Answer:
[tex] \red{- 12x(3x - 4)}[/tex]
Step-by-step explanation:
We know that,
[tex](a - b)^{2} = {a}^{2} - 2ab + {b}^{2} \\ [/tex]
Accordingly, let us solve the sum now.
[tex]16 - 4(3x - 2)^{2} \\ 16 - 4(9 {x}^{2} - 12x + 4) \\ 16 - 36 {x}^{2} + 48x - 16 \\ - 36 {x}^{2} + 48x \\ - 12x(3x - 4)[/tex]
1 point
Calculate the rate of change for each function over the interval [0, 3], then tell which function is
growing faster.
f(x) = 2x + 3
g(x) = 2² +3
Of(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So f(x) is growing faster
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So f(x) is growing faster
If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.
The correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
How to estimate the rate of change of a function over the interval [0, 3]?Let f(x) = 2x + 3 and g(x) = 2² +3
Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.
If f(x) = 2x + 3
Δy/Δx = [f(3) - f(0)]/3 - 0
f(3) [tex]= 2*3+3 = 9[/tex]
f(0) [tex]= 2*0+3 = 3[/tex]
[f(3) - f(0)]/3 - 0 = (9 - 3)/3
= 6/3 = 2
g(x) = 2² +3
Δy/Δx = [g(3) - g(0)]/3 - 0
[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]
[tex](2^3 +3)-(2^0 +3) = 7[/tex]
[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33
Therefore, the correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
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The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(0) = g(0) and f(2) = g(2)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer:
first option
Step-by-step explanation:
Always remember to graph a diagram :)
Calculate the slope of a line that goes through (3,3) and (8,1).
Answer:
slope formula= y2-y1/x2-x1
=1-3/8-3
= -2/5
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There are 50 pennies in a roll. if you have 110 rolls of pennies, how many pennies do you have?
Answer:
The answer to your question is 5500
Step-by-step explanation:
[tex]50x 110 = 5500\\[/tex]
I hope this helps and have a good day!
A study analyzed the average yearly salt intake in the united states from 2012 thru 2017. the data is summarized in the table: the study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the the number of years since 2012 and f(x) is the total amount of salt ingested in grams. describe the significance of 3,548.
The significance of 3,548 estimates the average grams of salt used in 2012.
A connection between independent variables and the dependent variable.is defined by the function.
Functions help to represent graphs and equations. A function is represented by two variables, one is dependent, and another one is an independent function.
The study discovered that the function can represent the data after the year 2012 as,
f(x) = 52.3x + 3,548
Where x is the number of years since 2012.
Hence, The significance of 3,548 estimates the average grams of salt used in 2012.
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Mr.jake and me. sebastian are business partners. they divided the ratio of 3:2 the profit is 24,000. how much did mr.jake receive ?
Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.
So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.
Thus, the total profit between them is 3x + 2x = 5x.
The total profit given is 24,000.
Thus, we get an equation:
5x = 24000,
or, x = 24000/5 = 4800.
Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.
Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.
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Can someone help me with this and show work pleaseee!!!
Answer:
10 units and 157.84 units
Step-by-step explanation:
4
substitute t = 1 into the equation
h = - 16(1)² + 6 = - 16 + 6 = - 10
the value is negative since the ball travels down
the ball has travelled 10 units after 1 second
5
substitute t = 3.2 into the equation
h = - 16(3.2)² + 6 = - 16(10.24) + 6 = - 163.84 + 6 = - 157.84
the well is 157.84 units deep
Solve the triangle. A = 46°, a = 31, b = 27
A. B = 38.8°, C = 115.2°, c ≈ 34.3
B. B = 38.8°, C = 95.2°, c ≈ 25.7
C. B = 38.8°, C = 95.2°, c ≈ 42.9
D. Cannot be solved
Answer:
C. B=38.8, C=95.2, c=42.9
Step-by-step explanation:
Find B by using sine rule
sin 46/31=sin B/27
sin B= 27 sin 46/31
B=sin‐¹(0.627)
B=38.8
Find C
C= 180-(A+B)
C=180-(38.8+46)
C=95.2
Using sine rule, Find c
31/sin 46=c/sin 95.2
c=31 sin 95.2/sin 46
c=42.9
Ryan called each school in the district to determine wether or not they have a recycling program. What is true about Ryan’s data collection
Ryan's data collection is true that Ryan did a survey he asked about qualitative data.
Given that Ryan called every school in the district to find out if they had a recycling program.
We know that there are two types of data:
Quantitative data deals with numbers and things that we can count or measure such as dimensions such as height, width, and length.
Qualitative data relating to characteristics and descriptions cannot be counted or measured, but are observable by their qualities such as smell, taste, and color.
If we ask for quantitative data, the survey will be quantitative. Data recycling means the quality of the data available.
They can ask for a yes or no answer, as in the Ryan investigation.
Hence, the correct statement about Ryan's data collection is: Ryan conducted a survey in which he asked about qualitative data.
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Derivatives with the functions of multiplication, division and rule of the chain. derive the following algebraic functions using all the basic formulas of algebraic derivatives (it is important to do the procedure) y=2x3+5x4x-9 y=3x+2x2+5 y=(5x2-9)6
The derivatives of y=[tex]2x^{3}+5x^{2} +4x-9[/tex] is [tex]6x^{2} +10x+4[/tex], derivative of y=[tex]2x^{2} +3x+5[/tex] is 4x+3, derivative of [tex](5x^{2} -9)6[/tex] is 60x.
Given three functions y= [tex]2x^{3}+5x^{2} +4x-9[/tex], y=[tex]2x^{2} +3x+5[/tex], y=[tex](5x^{2} -9)6[/tex].
We have to find the derivative of functions.
Derivative of a function of a real variablemearsures the sensitivity to change of the function value with respect to a chaneg in its argument. Derivatives are a fundamental tool of calculas.
First function: y=[tex]2x^{3}+5x^{2} +4x-9[/tex], derivative can be as under:
dy/dx=2*3[tex]x^{2}[/tex]+2*5x+4 (derivative of x is 1)
(d[tex]x^{n}[/tex]/dx=n[tex]x^{n-1}[/tex])
dy/dx=6[tex]x^{2}[/tex]+10x+4
Second function: y=[tex]2x^{2} +3x+5[/tex], derivative can be as under:
dy/dx=2*2x+3
=4x+3
Third function:y=[tex](5x^{2} -9)6[/tex]
dy/dx=5*2x*6
=10x*6
=60x
Hence the derivative of first function is [tex]6x^{2} +10x+4[/tex], second function is 4x+3, third function is 60x.
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Francisco's credit card has an APR of 13%, calculated on the previous
monthly balance, and a minimum payment of 2%, starting the month after the
first purchase. His credit card record for the last 7 months is shown in the
table below.
A.609.87
B.45.52
C.330.35
D.279.53
The amount of the $5200 charge that Francisco made during the first month has been paid off will be $279.53 based on the APR.
What is APR?Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors
For credit cards, the interest rates are typically stated as a yearly rate. This is called the annual percentage rate.
The amount of the $5200 charge that Francisco made during the first month has been paid off will be the total of the principal paid which is:
Principal paid = $47.67+$47.23+$46.80+$46.37+$45.94+$45.52
=$279.53
Therefore, the amount of the $5200 charge that Francisco made during the first month has been paid off will be $279.53.
In conclusion, the correct option is D.
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Complete question:
How much of the amount of the $5200 charge has Francisco paid off in the first month?