a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.
b. Sheila can afford the babysitter for 6 hours and 30 minutes.
c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.
d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
a. We assume the hours affordable to Sheila be x hours.
Per hour charge of the babysitter = $10.
Time taken by the babysitter traveling = 1.5 hours.
Therefore, total chargeable time = 1.5 + x.
Therefore, the total charge by the babysitter = $10(1.5 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 10(1.5 + x) = 80.
b. We are asked to determine the hours Sheila can afford to hire the babysitter.
We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.
Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.
10(1.5 + x) = 80,
or, 1.5 + x = 8,
or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.
Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.
c. Per hour charge of the new babysitter = $15.
Time taken by the new babysitter traveling = 1 hour.
Therefore, total chargeable time = 1 + x.
Therefore, the total charge by the new babysitter = $15(1 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 15(1 + x) = 80.
d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.
To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as follows:
15(1 + x) = 80,
or, 1 + x = 80/15,
or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.
Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
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Which is the graph of a logarithmic function?
The domain and range of the graph of a logarithmic function are;
Domain; 0 < x < +∞Range; The set of real numbers.How can the graph that correctly represents a logarithmic function be selected?The basic equation of a logarithmic function can be presented in the form;
[tex]y = log_{b}(x) [/tex]
Where;
b > 0, and b ≠ 1, given that we have;
[tex]y = log_{1}(x)[/tex]
[tex] {1}^{y} = 1[/tex]
The inverse of the logarithmic function is the exponential function presented as follows;
[tex]x = {b}^{y} [/tex]
Given that b > 0, we have;
[tex] {b}^{y} = x > 0[/tex]
Therefore, the graph of a logarithmic function has only positive x-values
The graph of a logarithmic function is one with a domain and range defined as follows;
Domain; 0 < x < +∞
Range; -∞ < y < +∞, which is the set of real numbers.
The correct option therefore has a domain as x > 0 and range as the set of all real numbers.
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Answer:
3 or C
Step-by-step explanation:
The answer above is correct.
A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rate in kilometers per minute? How many kilometers will the cyclist travel in 20 mins. Don’t round your answers
Answer:
0.35 km per minute, 7 km in 20 minutes
Step-by-step explanation:
1 hr = 60 minutes
21 km per 60 minutes = 21/60 = 0.35 km per minute
In 20 minutes: 0.35*20 = 7 km
can someone please help me
Answer:
Cos (3pi/4) =0.999154554
Sin (3pi/4)=0.041111762
Step-by-step explanation:
On your calculator there should be SIN and COS next to each other
#1 tap COS
#2 put your given numbers, in this case
COS(3pi/4) = 0.999154554
same goes for SIN
SIN (3pi/4)=0.041111762
A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)
A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex] is [tex]33.6million[/tex].
How can we find the population size ?
The projection of population growth in yeast is given by
[tex]N=N_{0} e^{rt}[/tex]
Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]
[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]
N is population size
Substitute the values
[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]
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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 ~
Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder yx and the planes zy and z0.
By using the triple integral, the wedge's volume is 4/15.
What is parabolic cylinder?A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.
According to the assertion:The wedge's volume, which the parabolic cylinder encloses, must be determined.
Consequently, as a result of the z=y form,
In addition to the specified boundary, the plane y=0 x = 0, z = 0.
For all of this, we are therefore in the first octant. additionally, the plane
x + y = 1 is a constraint.
Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.
The following would be written as a triple integral:
∫x=0 ∫y=0
∫z=0 dy dz dx
Once the values have been entered and the problem has been solved, we obtain the
[−4/15(1−x)^5/2] at x=0
The answer will then change to 4/15.
As a result, using the triple integral, the wedge's volume comes out to 4/15.
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please help me 20 points
Add up the number of students within the random sample data:
32+26+28+22 = 108
We can then use proportional fractions / cross-multiply to answer the question.
In a sample size of 108 students, 32 of them preferred Movie A.
There are 900 students in total.
[tex]\frac{32}{108} =\frac{x}{900}[/tex]
32*900 = 28800
108*x = 108x
108x = 28800
x = [tex]266\frac{2}{3}[/tex] or [tex]\frac{800}{3}[/tex]
In decimal form that is approximately 266.667 and round that to the nearest whole number, you get 267 students who would prefer Movie A.
Two people can paint a house in 14 hours. Working individually one of the people takes 2 hours more than it takes the other person to paint the house. How long would it take each person working individually to paint the house?
( You are supposed to get a quadratic equation and then solve that, but I don't know how to get to it.)
Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, we have that the rates are given as follows:
The together rate is 1/14.The separate rates are 1/d and 1/(d-2).Hence:
[tex]\frac{1}{d} + \frac{1}{d - 2} = \frac{1}{14}[/tex]
[tex]\frac{d - 2 + d}{d(d - 2)} = \frac{1}{14}[/tex]
d² - 2d = 28d - 28.
d² - 30d + 28 = 0
(d - 29)(d - 0.96) = 0.
Both d and d - 2 have to be positive, hence the solution is d = 29, and it would take each person working individually 27 and 29 hours to paint the house.
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Instructions: Find m
Check the picture below.
we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.
For the graph y = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined
How to determine the slope?The equation is given as:
y = 1
A linear equation is represented as:
y = mx + c
Where:
m represents the slope
By comparison, we have:
m = 0
The slope of the parallel line is:
Slope = m
This gives
Slope = 0
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/0
Slope = undefined
Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined
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A fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
How far (to the nearest km) is the port north of the reef?
From rectangular component, the distance of the port north of the reef is 25.9808 km.
What is the distance of the given point by rectangular component analysis ?It is given that a fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
Thus the direction of the fishing trawler is given to be 120° with respect to the movement of the trawler.
Resolving the direction by the horizontal and vertical components, we get
The horizontal component of distance is |30*cos(120°)| = 15 km
The vertical component of distance is |30*sin(120°)| = 25.9808 km
Thus as we have to find the north direction or the vertical component, the distance is 25.9808 km.
Therefore, from rectangular component, the distance of the port north of the reef is 25.9808 km.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
See
The point D is
3 units left from origin
x coordinate=-31 units up from origin
y coordinate=1The point is
(-3,1)Direct variation
Multiply k=2
k(-3,1)2(-3,1)(-6,2)Option A
1. Reflect Rectangle ABCD across the y-axis, then
translate it using the following rule:
(x,y) → (x-4, y - 3).
A B
D
с
-4 -2
4
2
ТУ
O
-2-
-4-
2
4
X
√x
A' (
B'(
C'(
D'(
A"(
B"(
C"(
D"(
)
)
)
)
PLS HELP ME WITH THIS
Answer:
See attached image
Step-by-step explanation:
Describe a relationship that can be modeled by the function shown in the table, and explain how the function models the relationship.
x ------ f(x)
1 ------ 4
4 ------ 8
9 ------ 12
16 ------ 16
25 ------ 20
B: Identify and interpret the key features of the function in the context of the situation you described in part A
The relationship that can be modeled by the function shown in the table is y = 4·√x
How to illustrate the information?f(x) is defined as a product of 4 into √x
4 × √1 = 4
4 × √4 = 8
4 × √9 = 12
4 × √16 = 16
4 × √25= 20
Therefore, the relationship is defined as y is 4 times the square root of x that is, y = f(x) = 4√x
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One of the reasons to use the bootstrap method is because the formula for the confidence interval is too hard to derive. Group of answer choices True False
The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.
What purposes serve the bootstrap method?A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.
The advantages of the bootstrap methodThe benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.
Therefore it can be concluded that the said query statement is true.
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4x – 9y = 7
–2x + 3y = 4
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
It's 2 (to get - 4x & 4x + - 4x = 0)
What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?
It's 3 (to get 9y & - 9y + + 9y =0)
Hope this helps!
If you gain 7 dollars every 65 second how long will it take to get 50000 dollars
Answer:
5 days
(the exact number of days below)
Step-by-step explanation:
65/7=9.28571429
9.28571429 sec = 1 dollar
464285.715 seconds=50000 dollars
464285.715 seconds=5.373677256944 days
Module 1: directions: respond to this question to demonstrate your understanding of the topic/content. be sure to provide adequate and relevant details learned in the module to support your response. pay close attention to organizing your response so it makes sense and uses correct grammar. your response should be at least 5-7 sentences at a minimum. question: given the two points (1,5) and (-2, -4), write a set of instructions for your younger cousin that determines the equation of the line in slope-intercept form (y=mx+b). be sure to write the equation.
The slope intercept form of the line whose points are (1,5) and (-2,-4) is y=3x+2.
Given two points of a line (1,5) and (-2,-4).
We have to form an equation in slop intercept form.
Equation is relationship between two or more variables which are expressed in equal to form.Equations of two variables looks like ax+by=c.
Point slope form of an equation is y=x+mc where m is slope of the line.
From two points the formula of equation is as under:
(y-[tex]y_{1}[/tex])=[tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex]*(x-[tex]x_{1}[/tex])
where [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] are the points.
Putting the values of [tex]x_{1}[/tex]=1, [tex]x_{2}[/tex]=-2, [tex]y_{1}[/tex]=5 and [tex]y_{2}[/tex]=-4.
y-5=(-4-5/-2-1)*(x-1)
y-5=-9/-3*(x-1)
y-5=3(x-1)
y-5=3x-3
y=3x-3+5
y=3x+2
Hence the slope intercept form of the line having points (1,5)(-2,-4) is y=3x+2.
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SOLVE FOR X AND THEN SOLVE FOR A
Answer:
Step-by-step explanation:
A + B= 180°
(5x+20)+(9x-92)=180°
14x-72=180°
14x=252
x=18
A=5(18)+20
A=110
Answer:
x = 18 , ∠ A = 110°
Step-by-step explanation:
∠ A and ∠ B are same- side interior angles and sum to 180° , that is
5x + 20 + 9x - 92 = 180
14x - 72 = 180 ( add 72 to both sides )
14x = 252 ( divide both sides by 14 )
x = 18
Then
∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°
Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)
The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction
Emanuel did a mistake in her first step by taking negative sign twice.
What is multiplicative rule with different sign ?Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.
Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.
For instance:
8 x 4 = 32(-8) x (-4) = 3210 x 9 = 90(-10) x (-9) = 90According to question,
= [tex]\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)[/tex]
Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.
Correct steps are:
Step 1:
[tex]\frac{(3)(4)(-1)}{(5)(9)(2)}[/tex]
Step 2:
[tex]\frac{-12}{90}[/tex]
Step 3:
[tex]-\frac{2}{15}[/tex]
Therefore, the step 1 was miscalculated by Emanuel.
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The complete question is -
Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)
Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction
Step 3 StartFraction 12 over 90 EndFraction
Step 4 StartFraction 2 over 15 EndFraction
In which step did his first error occur?
help me please guys!!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{|-8| + 9 = }[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8| + 9}[/tex]
[tex]\mathsf{= \bold 8 + 9}[/tex]
[tex]\mathsf{= 17}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{|-8 + 9| =}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8 + 9|}[/tex]
[tex]\mathsf{= -8 + 9}[/tex]
[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]
[tex]\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Let u - 4x? - 1. Find du. (4-1) du - Indicate how the limits of integration should be adjusted in order to perform the integration with respect to u. (Enter your answer using interval notation.) [0, 1] - Evaluate the definite integral. 01 Need Help? Read to a Tutor Consider the following. Let u = x + 1. Find du. du- Indicate how the limits of integration should be adjusted in order to perform the integration with respect to L. (Enter your answer using interval notation, [0, 2] - Evaluate the definite integral.
The value of du becomes 4 by integration.
According to the statement
we have given a two statement which are u - 4x and u = x + 1.
And we have to find the value of du by the use of integration.
An Integral assigns numbers to functions in a way that describes the data.
So,
From u - 4x
here du becomes by derivative
du - 4dx/du
du = 4dx/du. -(1)
And in u = x + 1.
here du becomes
du = dx/du -(2)
by comparing both terms from equation (1) and (2) we get the value of du
du = 4.
the value of du is 4.
So, The value of du becomes 4 by integration.
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what is the derivative of this
The derivative of the natural logarithm function is given by:
[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]
What is the derivative of the natural logarithm function?Suppose we have a composite natural logarithm function given as follows:
[tex]f(x) = \ln{g(x)}[/tex]
The derivative of the function is given as follows:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]
In this problem, the function, which is already a first derivative, it given by:
[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]
The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:
[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]
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When given an inverse variation, how do you find k?
Find the polynomial function in standard form that has the zeros listed. i and -i
The polynomial function in standard form that has the zeros listed. i and -i is x² +1 = 0.
What is polynomial function?A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.
The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Calculation for the polynomial function-
The general two degree/quadratic equation is given by-
ax² + bx + c = 0
Where a ≠ 0
If the two roots of the equation are x1 and x2.
Then the relation between roots and coefficients of the polynomial are -
The sum of the roots = (- coefficient of x)/(coefficient of x²)x1 + x2 = (-b)/a
The multiplication of the roots = constant/coefficient of x²x1.x2 = c/a
From the above two relation the general equation can be written as-
x² -(x1 - x2)x + x1.x2 = 0
Lets say x1 = i and x2 = -i
Substitute the values of x1 and x2 in the general equation
x² -(i - i)x + (i).(-i) = 0
x² - i ² = 0
x² + 1 = 0
Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.
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PLS HELP ASAP
whats relationship between a and b
The correct answer is none of the above.
What is a line?A line is defined as the shortest distance between two points and the point where two lines meet is known as an angle.
From the given figure, the measure of angle a and b are supplementary since the sum of the angles is not 180 degrees.
They are not vertical angles since they do not meet at a point of intersection
The measure of angle a and b are complementary since the sum of the angles is not 90 degrees. Hence the correct answer is none of the above.
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Dalvin took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $2 per mile. The total fare was $30.80, not including the tip. Which tape diagram could be used to represent the context if mm represents the number of miles in the taxi ride?
Answer:
The equation should be 2.5x+1.8=59.3
Step-by-step explanation:
The number of miles in the taxi ride is 10
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Dalvin took a taxi from his house to the house. The taxi company charged a pick-up fee of $4.80;
The fare per mile is $2
The total fare was $30.80, not including the tip;
Let the number of mile is x
Total fare = pick up fee + fee per mile
30.80 = 4.80 + 2x
2x = 26
x = 13
Therefore, the number of miles by algebra Dalvin took a taxi will be 13
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Someone help pls, its urgent! ASAP!! (Geometry)
“Complete the proofs”
Question 8
1) [tex]\triangle ACE[/tex] with [tex]\overline{AC} \cong \overline{EC}[/tex], [tex]\overline{BC} \cong \overline{DC}[/tex] (given)
2) [tex]\angle C \cong \angle C[/tex] (reflexive property)
3) [tex]\triangle ACD \cong \triangle ECB[/tex] (SAS)
Question 9
1) [tex]\overline{PQ}[/tex] and [tex]\overline{PR}[/tex] are the legs of isosceles [tex]\triangle PQR[/tex], [tex]\overline{PS} \cong \overline{QR}[/tex] (given)
2) [tex]\angle PSQ[/tex] and [tex]\angle PSR[/tex] are right angles (definition of perpendicular lines)
3) [tex]\angle Q \cong \angle R[/tex] (angles opposite the legs of an isosceles triangle are congruent)
4) [tex]\overline{PS} \cong \overline{PS}[/tex] (reflexive property)
5) [tex]\angle PSQ \cong \angle PSR[/tex] (all right angles are congruent)
6) [tex]\triangle PSQ \cong \triangle PSR[/tex] (AAS)
Question 10
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AB} \perp \overline{BC}[/tex], [tex]\overline{CD} \perp \overline{AD}[/tex] (given)
2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
3) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle ABC \cong \triangle CDA[/tex] (HL)
6) [tex]\overline{AD} \cong \overline{CB}[/tex] (CPCTC)
Question 13 (2 points)
Is there a value of a such that f(x) = 9x² +4 and g(x) = (3x-a)² are equivalent?
Explain. (show your work).
Answer:
Step-by-step explanation:jneke
There is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
What are equivalent polynomials?Two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.
How to solve the question?In the question, we are asked is there a value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
We know that two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.
Thus to check, we expand g(x), using the formula (p - q)² = p² + q² - 2pq.
g(x) = (3x - a)²,
or, g(x) = (3x)² + (a)² - 2(3x)(a),
or, g(x) = 9x² + a² - 6ax.
For f(x) = 9x² - 4, and g(x) = (3x - a)² to be equivalent,
-6ax should be 0, that is, a should be 0,a² should be 4, that is, a needs to be 2, or -2.As we need two different values of, 'a' at the same time, which ain't possible, thus we can say that there is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.
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A container is the shape of an inverted right circular cone has a radius of 4.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 2.00 inches deep, the surface level is falling at the rate of -2.00 in./s. Find the rate at which water is being drained.
The rate at which the water from the container is being drained is 24 inches per second.
Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.
Looking at the image we can use similar triangle propert to derive the relationship:
r/R=h/H
where dh/dt=2.
Thus r/5=2/5
r=2 inches
Now from r/R=h/H
we have to write with initial values of cone and differentiate:
r/5=h/5
5r=5h
differentiating with respect to t
5 dr/dt=5 dh/dt
dh/dt is given as 2
5 dr/dt=5*-2
dr/dt=-2
Volume of cone is 1/3 π[tex]r^{2} h[/tex]
We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.
Thus
dv/dt=1/3 π(2rh*dr/dt)+([tex]r^{2}[/tex]*dh/dt)
Putting the values which are given and calculated we get
dv/dt=1/3π(2*2*2*2)+(4*2)
=1/3*3.14*(16+8)
=3.14*24/3.14
=24 inches per second
Hence the rate at which the water is drained from the container is 24 inches per second.
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