Answers
ANSWER
EXPLANATION
We have that the line EG = 71.
We are given that
EF = 8x - 17
and
FG = 5x - 3
We see from the diagram that:
EF + FG
Related Questions
The mean phone bill is $______The median phone bill is $______Determine the mode phone bill. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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Given: $36.52,$42.30.$39.78. $38.26. $44.39, $49.55
to find: Mean , Median and mode
soluiton:
Since, formula for mean
[tex]=\frac{su\text{m of all terms}}{nu\text{mber of terms}}[/tex]Here, sum of all terms = 36.52 + 42.30 + 39.78 + 38.26 + 44.39 + 49.55 = 250.8
number of terms = 6
Thus,
[tex]\operatorname{mean}=\frac{250.8}{6}=41.8[/tex]Hence, mean of phone bill is $41.8
Since, number of terms = 6 which is even
so, median
[tex]=\mleft\lbrace\frac{\frac{n}{2}+(\frac{n}{2}+1)th\text{ term}}{2}\mright\rbrace[/tex]arranging the terms in ascending order: 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
Now, median
[tex]\begin{gathered} =\mleft\lbrace\frac{3rd+4th\text{ term}}{2}\mright\rbrace \\ =\frac{39.78+42.30}{2} \\ =41.04 \end{gathered}[/tex]Hence, median of the phone bill is $41.04
Mode:
Given terms are 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
If no value or number in the data set appears more than once, then it has no mode
Hence, the phone bill has no mode
Describe two methods you could use to solve for `x` in `1.12^{x}=20`
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EXPLANATION:
Given;
We are given the following equation;
[tex]1.12^x=20[/tex]Required;
We are required to describe two methods which can be used to solve for x in this equation.
Step-by-step solution;
We can solve for the variable x by taking the natural log of both sides of the equation. This is shown below;
[tex]1.12^x=20[/tex]We take the natural log of both sides;
[tex]ln1.12^x=ln20[/tex]Next we apply the log rule;
[tex]\begin{gathered} If: \\ log_bx^a \\ Then: \\ alog_bx \end{gathered}[/tex]Therefore, our equation is now refined and becomes;
[tex]xln1.12=ln20[/tex]Divide both sides by ln(1.12);
[tex]x=\frac{ln(20)}{ln(1.12)}[/tex]A second method is to express it as a logarithmic equation;
[tex]1.12^x=20[/tex]We shall apply the log rule which is;
[tex]\begin{gathered} If: \\ log_bx=a \end{gathered}[/tex][tex]\begin{gathered} Then: \\ b^a=x \end{gathered}[/tex]For example;
[tex]\begin{gathered} If: \\ log_{10}100=2 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ 10^2=100 \end{gathered}[/tex]Therefore, for the equation given;
[tex]\begin{gathered} If: \\ 1.12^x=20 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ log_{1.12}20=x \end{gathered}[/tex]Note that both solutions can be simplified eventually with the use of a calculator.
ANSWER:
(1) By taking the natural log of both sides
(2) By expressing the equation as a logarithmic equation
Identify the vertex, intercepts and whether of the graph of the function below opens up or down. Type your answers as a point (x,y). If an intercept does not exist type "none". If more than one intercept exists you can type either intercept.f(x)= -|x-9|+16 Vertex = Answerx intercept = Answery intercept = Answergraph opens Answer
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The absolute value function :
[tex]f(x)=\pm\lvert x-h\rvert+k[/tex]has a vertex at (h, k) and it opens upward if the sign before the absolute value sign is positive. It open downward if the sign is negative.
From the problem, we have :
[tex]f(x)=-\lvert x-9\rvert+16[/tex]The vertex will be (9, 16)
x intercept is the value of x when f(x) = 0.
Set f(x) = 0 and solve the value of x.
[tex]\begin{gathered} 0=-\lvert x-9\rvert+16 \\ \lvert x-9\rvert=16 \end{gathered}[/tex]In solving absolute values, you will get two values, one for the positive and one for the negative.
[tex]\begin{gathered} x-9=16 \\ x=16+9 \\ x=25 \end{gathered}[/tex][tex]\begin{gathered} x-9=-16 \\ x=-16+9 \\ x=-7 \end{gathered}[/tex]The x-intercepts are (-7, 0) and (25, 0)
y-intercept is the value of f(x) when x = 0.
Set x = 0, and evaluate f(x)
[tex]\begin{gathered} f(x)=-\lvert0-9\rvert+16 \\ f(x)=-9+16 \\ f(x)=7 \end{gathered}[/tex]The y-intercept is (0, 7)
The sign before the absolute value sign is negative, so it opens downward
Which of the following has the same value as cos 2pi/3
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First, let's calculate the value of cos 2pi/3:
[tex]\cos\frac{2\pi}{3}=-0.5[/tex]Now, let's calculate the value of each option:
[tex]\begin{gathered} \cos\frac{\pi}{6}=0.866\\ \\ \\ \\ \cos\frac{4\pi}{3}=-0.5\\ \\ \\ \\ \sin\frac{5\pi}{3}=-0.866\\ \\ \\ \\ \sin\frac{7\pi}{6}=-0.5\\ \\ \\ \\ \cos\frac{11\pi}{6}=0.866 \end{gathered}[/tex]Therefore the correct options are B and D.
Consider this system of linear equations:y = 4/5x - 3y = 4/5x + 1Try solving the system of equations algebraically and describe the result you get.
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the system has not solution
Explanation
[tex]\begin{gathered} y=\frac{4}{5}x-3 \\ y=\frac{4}{5}x+1 \end{gathered}[/tex]Step 1
to solve this we can use, Equalization, It consists in isolating from both equations the same unknown factor to be able to equal both expressions, obtaining one equation with one unknown factor.
[tex]\begin{gathered} \text{set y=y} \\ so \\ \frac{4}{5}x-3=\frac{4}{5}x+1 \\ \text{subtract 4/5 of x in both sides} \\ \frac{4}{5}x-3-\frac{4}{5}x=\frac{4}{5}x+1-\frac{4}{5}x \\ -3=1 \end{gathered}[/tex]we got that
-3=1, it is false, which means there are no values that satisfy the equation, I n other words
the system has no solution
I hope this helps you
A rectangular piece of metal has an area of 112 square centimeters. Its perimeter is 46 centimeters. What are the dimensions of the piece?
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Let the length of rectabgle be l and width of rectangle be b.
The equation for the area of rectangle is,
[tex]l\cdot b=112[/tex]The equation for perimeter of rectangle is,
[tex]\begin{gathered} 2(l+b)=46 \\ l+b=23 \\ l=23-b \end{gathered}[/tex]Substitute 23 - b for l in the equation lb
6000 divided by 80 (explain and do work)
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we can cancel a zero, because it is a common number
we take 60 because 6 is less than 8, 7x8 is very close to 60 obtain the result and substract from 60
go down the zero and look for a number that multiplied by 8 make 40
so,8x5=40
the solution of the division is 75
Answer:
75
Step-by-step explanation:
6 / 8 = 7.5
so 6000/80 = 75
write log_4 10 as a quotient of natural logarithms.ln__ln__
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We have to use the change-of-base formula of logarithms to simply write this log.
The logarithm to convert is:
[tex]\log _410[/tex]The change of base formula (using natural logarithms) is:
[tex]\log _ab=\frac{\ln b}{\ln a}[/tex]Matching this with the logarithm, we can write it as:
[tex]\log _410=\frac{\ln 10}{\ln 4}[/tex]The graph of the function F is shown above. What is limF(x)?
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Answer:
4
Explanation:
To evaluate a limit, we look at both right and left limi s. If the left and right limits both approach the ssme value, then the limit exists. t
As can be observed from the graph, as we reach x = 2 from the right, the functionseems to reach y = 4. In other other words,
[tex]\lim_{x\to2^+}f(x)=4[/tex]Note the tiny plus sig in the limit . This tells us that we are approaching the limit from the right.
Now let us take a look atthe rleft-hand limit.
Now as we approach x = 2 from the left we see that the function seems to take the value y =4. In other words,
[tex]\lim_{x\to2^-}^f(x)=4.[/tex]Note also the tiny negative sign in the limit. This tells us that we are approaching the limit from the left.
Now both the left and the right-hand limits approach the same value; therefore, the limit exists and its value is the following.
[tex]\boxed{\lim_{x\to2}f(x)=4.}[/tex]A circle with a radius of 3.9 cm is centered at the vertex of an angle.Suppose the angle has a measure of 175 ____degrees.What is the radian measure of this angle?____ radians What is the length (in cm) of the arc subtended by the angle's rays along the circle?_____ cm Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle. (Enter "theta" for θ.) ______cm
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We can draw the following picture:
From the angle-arc relationships, since the vertex is at the center of the circle, then the arc is equal to 175 degrees.
In radians, 175 degrees is equivalent to
[tex]175=175\cdot(\frac{\pi}{180})\text{rad}[/tex]that is
[tex]175=3.054\text{ rad}[/tex]What is the radian measure of this angle? 3.054 radians
The arc-lengh S is given by
[tex]s=r\cdot\theta[/tex]where, r=3.9cm and theta is equal to 3.054 rad (which is 175 degrees but in this formula the number must be written in radians). By sustituting these value, we have
[tex]\begin{gathered} s=(3.9)(3.054) \\ s=11.91\text{ cm} \end{gathered}[/tex]What is the length (in cm) of the arc subtended by the angle's rays along the circle? 11.91 cm
Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle.
We wrote the formula above:
[tex]s=r\cdot\theta[/tex]where s is the arc-lenght, r is the radius and theta is the angle (in radians).
laws of exponent : multiplication and power to a powerquestion 2)))-2r⁵ • 6r ⁻⁸
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You need to remember the following:
- The Product of powers property states that:
[tex]b^m\cdot b^n=b^{(m+n)}[/tex]- According to the Negative exponent rule:
[tex]b^{-m}=\frac{1}{b^m}[/tex]Given the following expression:
[tex](2r^{5})(6r^{-}^{8})[/tex]You can simplify it as following:
1. Multiply the coefficients.
2. Apply the Product of powers property.
3. Apply the Negative exponent rule.
Then, you get:
[tex](2r^{5})(6r^{-}^{8})=12r^{(5-8)}=12r^{-3}=\frac{12}{r^3}[/tex]The answer is:
[tex]\frac{12}{r^3}[/tex]The graph below shows the solution to which system of inequalities?A. x< 1 and y2 xB. ys 1 and y>xC. x≤ 1 and y> xD. y< 1 and y2
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To answer this question let's look at each line first.
The slant line can be express by the equation:
[tex]y=x[/tex]We notice that the shaded part is above this line, then we have that that inequality is written as:
[tex]y\ge x[/tex]Now, the horizontal line is express as:
[tex]y=1[/tex]since the shaded region is below that line and the line is dashed the inequality is:
[tex]y<1[/tex]Therefore, the system of inequalities is:
[tex]\begin{gathered} y\ge x \\ y<1 \end{gathered}[/tex]mmhey again um yea i looked at my notes but thats not really helpful :/
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We have the following:
Since the sides are equal, it means that all the angles are equal, we also know that the sum of the 3 angles within a triangle is always 180°, therefore
[tex]\begin{gathered} 5x+5x+5x=180 \\ \text{solving for x:} \\ 15x=180 \\ x=\frac{180}{15} \\ x=12 \end{gathered}[/tex]The value of x is 12
please help with this i will attach photo of figure
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The variable I=f(w) represents the number of individuals (in thousands) infected w weeks after the epidemic begins.
The value of I=f(2) represents the number of individuals in thousandas infected 2 weeks after the beginning of the epidemic.
From the graph, where I=8, we can conclude that there are 8,000 infected people after 2 weeks of the beginning of the epidemic.
Answer:
f(2) = 8
Means 8,000 people are infected after 2 weeks of the beginning of the epidemic.
Find the surface area of the cylinder below. Use 3.14 for l~l. round your answer to the nearest tenth.
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Out of 167 randomly selected adults in the United States who were surveyed, 70 exercise on a regular basis. Construct a 90% confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places
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ANSWER:
(0.356, 0.482)
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the proportion with the data of the statement:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{70}{167} \\ \\ p=0.4192 \end{gathered}[/tex]For a 90% confidence interval, we have that the value of Z is the following:
[tex]\begin{gathered} \alpha=1-90\% \\ \\ \alpha=1-0.9=0.1 \\ \\ \alpha\text{/2}=\frac{0.1}{2}=0.05 \\ \text{ } \\ \text{The corresponding value of Z would be:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the interval as follows:
[tex]\begin{gathered} \text{ Upper limit }=p+Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192+1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.482 \\ \\ \text{ Lower limit}=p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192-1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.356 \end{gathered}[/tex]The 90% confidence interval for the proportion of all adults in the United States is (0.356, 0.482)
Determine the linear equation of the vertical and horizontal line passing through the point (5,8).
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Given:
The horizontal and vertical line psses through the point (5,8).
To find:
Find the equation of vertical and horizontal line passing through the given point.
Equation of vertical line:
[tex]x=5[/tex]Equation of horizontal line:
[tex]y=8[/tex]Determine the correct order of the numbers from least to greatest. 1.3, -2.875, 6.75, -4, -1.67, -3.75, 3.5
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By definition, the Positive numbers are those numbers greater than zero and Negative numbers are those numbers less than zero.
Therefore, you know that the Positive numbers are greater than the Negative numbers.
For this exercise it is also important to remember that the Absolute value of a number tells you its distance from zero on the Number line. The Absolute value of a number is always positive.
Knowing the above, you can set up that:
[tex]-4<-3.75<-2.875<-1.67<1.3<3.5<6.75[/tex]Remember that this symbol means "Less than":
[tex]<[/tex]The answer is:
[tex]-4,-3.75,-2.875,-1.67,1.3,3.5,6.75[/tex]{(-2, 5), (-1, 2), (0, 1), (2,5)}
Which points are on the graph of the inverse?
Select each correct answer.
(5,2)
(2, 1)
-
(-5, 2)
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let's recall that the domain of a function is the range of its inverse function, namely, the inverse has a pair that's just the same but flipped sideways, Check the picture below.
changing the value of b in f(x)=mx+b results in a translation or reflection?
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8. The chart below shows the student lunch menu at a school. A lunch consists of onesandwich, one snack, and one drink.Lunch MenuSandwichSnack Drinkturkey apple juicebologna bananamilkpeanut buttercookieshamyogurtHow many different lunch choices does a student have?hirtants and subite or
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We have to find all the different lunch choices that a student have, where one lunch consists of one sandwich, one snack, and one drink.
For doing so, we remember the multiplication principle. As for each option of sandwich, we have _ options for the snacks, and for each snack we have _ options of drinks, we just have to multiply each one of the values. In this case,
Because there are 3 feet in every yard, the formula F = 3 ⋅ Y will convert Y yards into F feet. Find F ifY = 5 yards5 yards converts to ? feet.
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The problem says that
[tex]\text{feet}=3\cdot\text{yards}[/tex]Then, if we want to convert yards to feet, we got to multiply it by three. The question is, how many feet is 5 yards? let's use the formula:
[tex]\begin{gathered} \text{feet}=3\cdot5 \\ \\ \text{feet}=15 \end{gathered}[/tex]Therefore, 5 yards is 15 feet
I need to know the scale factor and what S is.
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In order to find the scale factor between the triangles, we can compare the sides PR and PT, which are corresponding sides between the triangles.
The side PR has a length of 27 units, and the side PT has a length of 9 units, so we can find the scale factor by dividing one length by the other:
[tex]\text{scale factor}=\frac{PR}{PT}=\frac{27}{9}=3[/tex]Now that we have the scale factor, we can find the length of PS by comparing it with the corresponding side PQ:
[tex]\begin{gathered} \text{scale factor}=\frac{PQ}{PS} \\ 3=\frac{24}{PS} \\ PS=\frac{24}{3}=8 \end{gathered}[/tex]If the length of PS is 8 units and S is above the x-axis to the right, its coordinates will be (8, 0).
Not a timed or graded assignment. Need full work shown. Quick answer with work = amazing review
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The Solution:
Given the expression below:
[tex]10\text{ }\sqrt[]{112m^6}[/tex]We are asked to simplified in radical form.
Let's find the factors of 112.
[tex]\begin{gathered} 112=2\times56 \\ =2\times2\times28 \\ =2\times2\times2\times14 \\ =2\times2\times2\times2\times7 \end{gathered}[/tex][tex]\sqrt[]{m^6}=\sqrt[]{m^3\times m^3}[/tex]So,
[tex]\sqrt[]{112m^6}=\sqrt[]{112\times m^3\times m^3}=\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}[/tex][tex]10\sqrt[]{112m^6}=10\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}=10(2\times2\times m^3)\text{ }\sqrt[]{7}[/tex]Thus,
[tex]10\sqrt[]{112m^6}=\text{ }10(2\times2\times m^3)\text{ }\sqrt[]{7}=10(4)m^3\text{ }\sqrt[]{7}=40m^3\text{ }\sqrt[]{7}[/tex]Therefore, the correct answer is
[tex]40m^3\text{ }\sqrt[]{7}[/tex]what is the slope and the y-intetercept of each problemy= -2x - 3y= -2x + 2
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Answer:
• m=-2, b=-3
,• m=-2, b=2
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]Part A
Given the equation:
[tex]y=-2x-3[/tex]• The slope, m = -2
,• The y-intercept, b=-3
Part B
Given the equation:
[tex]y=-2x+2[/tex]• The slope, m = -2
,• The y-intercept, b=2
a. Determine whether the equation x/4-x/3=1 is a linear equation. If yes, identify the equation in standard form.
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The given equation is a linear equation and its standard form is [tex]3x-4y=12[/tex].
The given equation is -
[tex]\frac{x}{4}-\frac{y}{3}=1[/tex] ---- (1)
We have to determine if the given equation is a linear equation. If it is a linear equation, then we have to write it in standard form.
A linear equation is referred to as the equation of a straight line.
A linear equation with two variables can be written in the standard form as
[tex]ax+by=c[/tex]
where a, b, c are constants
and, x, y are variables
So, from equation (1), we can say that -
The equation [tex]\frac{x}{4}-\frac{y}{3}=1[/tex] is a linear equation.
Identifying the equation in standard form, we have
[tex]\frac{x}{4}-\frac{y}{3}=1\\= > \frac{3x-4y}{12}=1\\ = > 3x-4y=12[/tex]
Hence, the standard form of the given linear equation is [tex]3x-4y=12[/tex].
To learn more about linear equation visit https://brainly.com/question/13738061
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Help n k oh hi k. Hi hold kb b g g I
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SOLUTION:
[tex]v(n)=(14)\cdot b^n[/tex]The correct answer is;
If b = 1.06, the weekly growth rate of the share's value is 6%
In a raffle, one ticket will win a $930 prize, and the other tickets will win nothing. There are 500 in the raffle, each costing $6. If you buy a ticket, what is the expected profit?
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Which equation is nonlinear? x=-4 y= 0 y= 2/3x- 2 y= ײ +1
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equationWhich equation is nonlinear?
x=-4
y= 0
y= 2/3x- 2
y= ײ +1
__________________
Linear eqaution form
y = mx +b
x=-4 (Line)
y= 0 (lineon the axis)
y= 2/3x- 2 (This is a linear equation )
_____________________
Answer
y= ײ +1
2. Which statement is an example of a transitive relationship? If ctm and m || n, then cin. If x = 2y and 2y 8, then x = 4. If a Il band b || c, then a || o. If min and mlp, then m || p.
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A relationship is said to be transitive, if
a R b, b R c, then → a R c.
Test the given options
For the first option, if x = 2y and 2y = 8, then for transitive relationship,
[tex]\begin{gathered} x=2y \\ 2y=8 \\ then,x=8 \end{gathered}[/tex]the first option is not correct because x ≠ 4
For the second option, If a Il b and b || c, then a || c
[tex]\begin{gathered} a\text{ R b means that a is parallel to b} \\ b\text{ R c means that b is parallel to c} \\ a\text{ R c means that a is parallel to c} \end{gathered}[/tex]Looking at the second option, there is a relationship of parallelism between a, b and c, therefore, this is a transitive relationship
For the third option
If m ⊥ n and m ⊥ p, then m ∥ p.
The statement from the point of view of transitive relationship is incorrect
it should be, n ⊥ p.