1)Lin solved the equation incorrectly. Find all the errors in her solution. (Select all appropriate answers.)Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.Step 1 to Step 2: Lin distributed 8(x - 3) incorrectly; should be 8x - 3.Step 2 to Step 3: Lin calculated 8x - 24 + 7 incorrectly; should be 8x - 31.Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.What should Lin's answer have been ?8 ( x - 3 ) + 7 = 2x ( 4 - 17 )answer choices :x = 3/2 x = 1/2x = 1/5x = 1/3
Answers
Answer:
Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.
Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.
Lin's answer should be x = 1/2
Explanation:
The initial expression is:
8(x - 3) + 7 = 2x(4 - 17)
So, the first error is in step 1, because 4 - 17 = - 13, then step 1 should be:
8(x - 3) + 7 = 2x(-13)
Then, we can apply the distributive property as:
8x - 8(3) + 7 = -26x
8x - 24 + 7 = -26x
We need to add similar terms:
8x - 17 = - 26x
Then, we can subtract 8x from both sides as follows:
8x - 17 - 8x = - 26x - 8x
-17 = -34x
Finally, we can divide by -34 as follows:
-17/(-34) = -34x/(-34)
1/2 = x
Therefore, the answers are:
Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.
Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.
Lin's answer should be x = 1/2
Related Questions
write the equation of the line using the given slope and pointm=4 (2,6)
Answers
1) We can write the equation of the line, using this point (2,6) and the slope m=4.
2) So, let's plug into the slope-intercept form the point and the slope to find the y-intercept
[tex]\begin{gathered} y=mx+b \\ 6=4(2)+b \\ 6=8+b \\ 6-8=b \\ b=-2 \end{gathered}[/tex]3) Thus, we can write out the following equation:
[tex]y=4x-2[/tex]Find three odd consecutive integers whose sum is 531
Answers
The number = 531
There are no three consecutive odd integers whose sum is 531
Because the difference between consecutive integer is 1
What is the probability that a student would randomly choose a school uniform outfit with a plaid skirt and black sneakers ?
Answers
Notice that as for the type of shoes, there are two possibilities either loafers or black sneakers.
Therefore, the probability of choosing black sneakers is 0.5.
On the other hand, after picking the black sneakers, there are 4 possibilities as to the sort of skirt/pants to use, and the probability of choosing a plaid skirt is 1/4=0.25.
Thus, the probability of randomly choosing a plaid skirt and black sneakers is
[tex]P(sneakers\cap plaid)=0.5*0.25=0.125[/tex]Therefore, the answer is 0.125 or 1/8 (both are correct).1. Given that f(x)=x²-4 and that g(x)=√√x-1:
A. State (f-g)(x) and (fog)(x).
B. State
and determine its domain.
C. Determine whether each of the following functions is odd, even, or neither odd nor
even: f(x)=x²-4, g(x)=√√x-1.
D. State (g/f)(x) and find all vertical asymptotes.
Please show work! Thank you so much!
Answers
Given the functions are,
[tex]f(x)=x^2-4\\g(x)=\sqrt[3]{x-1}[/tex]
Then the subtraction of functions is given by,
[tex](f-g)(x)=f(x)-g(x)=x^2-4-\sqrt[3]{x-1}[/tex]
Again,
[tex](f\circ g)(x)=f(g(x))=f(\sqrt[3]{x-1})=(x-1)^{2/3}-4[/tex]
And,
[tex]\left(\frac{f}g{}\right)(x)=\frac{f(x)}{g(x)}=\frac{x^2-4}{\sqrt[3]{x-1}}[/tex], it exists when x not equals to 1.
So domain of the function is all real number except 1.
Since, [tex]f(-x)=(-x)^2-4=x^2-4=f(x)[/tex], then the function is an even function.
Since [tex]g(-x)=\sqrt[3]{-x-1}[/tex], so it is neither odd function nor even function.
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what is 1 + 1 and two times 15
Answers
Solution
1 + 1= 2
2* 15= 30
3. Factor 3x from 12x2 + 15x 3
Answers
SOLUTION
In this question, we are meant to factor
[tex]\begin{gathered} 3xfrom12x^2+15x^3 \\ \text{Next, we factor in this manner,} \\ 3\text{ x ( }4x+5x^2\text{ )} \\ \text{CONCLUSION : The correct solution is 3 x ( 4 x + 5 x }^2\text{ )} \end{gathered}[/tex]Find the surface area of this cone. I think the inside is hollow? Im not sure what to do with this problem to be honest
Answers
Let us start this problem by analyzing the area we want to calculate
.
To calculate the surface area we will divide the are in two parts:
[tex]\text{ The total area = Area of the base + area of the inner and outer cone}[/tex]The area of the base:
The area of the base can be calculated as the difference between the areas of the to disks , as follows:
[tex]\begin{gathered} \text{ Area of the base=Area of the outer disk - area of the inner disk} \\ =\pi(12)^2-\pi4^2 \\ \\ =128\pi \\ \end{gathered}[/tex]Where we use twice the formula for the area of a circle pi*radius^2, for the outer disk the radius is 12 and for the inner disk the radius is 4.
The lateral area of the two cones, the outer and the inner
Now we will calculate the lateral area of a cone (that is we will not include the base) this area is illustrated by the following draw:
The lateral area of a cone can be calculated using the next formula
[tex]\text{ Lateral area of a cone=}\pi r\sqrt{h^2+r^2}[/tex]Where h is the height of the cone, and r is the radius of the base, for the bigger cone we know from the figure that the height is 6 ft and the radius is 12 ft, for the smaller cone we also know from the figuere that the height is 3 ft and the radius is 4 ft. Therefore we can calculate:
[tex]\begin{gathered} \text{ Lateral area of the bigger cone= }\pi12\sqrt{6^2+12^2} \\ \\ =12\pi\sqrt{180} \end{gathered}[/tex]and
[tex]\begin{gathered} \text{ Lateral area of the smaller cone= }\pi4\sqrt{3^2+4^2} \\ \\ =4\pi\sqrt{25} \\ \\ =20\pi \end{gathered}[/tex]Finally, putting all the areas together we find that:
[tex]\begin{gathered} \text{ The total area= The area of teh base+ the lateral area of the two cones} \\ \\ =128\pi+12\sqrt{180}\pi+20\pi \\ \\ =148\pi+12\sqrt{180}\pi \\ \\ =148\pi+72\sqrt{5}\pi \end{gathered}[/tex]A car company charges $42.50 per day to rent a car in 10 since for every mile driven Lydia wants to rent a car knowing that she plans to drive 225 miles and she has at most a $150 to spend
Answers
Explanation:
d: number of days.
m: number of miles.
The total cost of the car 'y' is:
[tex]y=42.5d+0.1m[/tex]Lydia plans to drive 225 miles, this is m = 225. And she has $150 to spend, so we have to solve y ≤ 150.
The inequality to solve is:
[tex]\begin{gathered} y\le150 \\ 42.5d+0.1\cdot225\le150 \\ 42.5d+22.5\le150 \end{gathered}[/tex]Solving the inequality:
[tex]\begin{gathered} 42.5d+22.5\le150 \\ 42.5d\le150-22.5 \\ 42.5d\le127.5 \\ d\le\frac{127.5}{42.5} \\ d\le3 \end{gathered}[/tex]Lydia can afford 3 days at most.
Answers:
• Inequality: ,42.5d + 22.5 ≤ 150
,• d ≤ 3
Need help with dilations mix
Answers
When you add/subtract values to the coordinates of a figure, its size doesn't change, you only move it to another location.
When you multiply the coordinates of a figure, you enlarge it, i.e. create a bigger figure proportional to the original one.
When you divide the coordinates of a figure, you reduce its size.
Since the figure was dilated and not moved, option F is incorrect.
To determine how much it was dilated select any point from the pre image and image and compare them.
For example
G (-2,1)
G'(-5,2.5)
To determine the coefficient used for the dilation divide the x-coordinate of the image point by the x-coordinate of the preimage point:
[tex]\frac{X_{G^{\prime}}}{X_G}=\frac{-5}{-2}=\frac{5}{2}[/tex]Now do the same to determine the coefficient used in the Y-coordinates:
[tex]\frac{Y_{G^{\prime}}}{Y_G}=\frac{2.5}{1}=2.5[/tex]2.5 expressed in fractions is 5/2
So the dilation made was (X,Y)→(2/5X,2/5Y)
The correct answer is E.
Question 3: 11 ptsArating for the school bus, Bruce records the colors of all cars passing through an intersection. The tablethe results. Estimate the probability that the next car through the intersection will be black. Express youras a percent. If necessary, round your answer to the nearest tenth.
Answers
To find the probability that the next car through the intersection will be black divide the number of black car by the total number of cars.
The total number of cars is the sum of the number of cars of each color, which is 58.
[tex]P=\frac{9}{58}=0.155[/tex]Expressed as a percent it is 15.5%.
It means that the correct answer is the last choice.
f(x) = -x^2 + x + 13Find f(9)
Answers
To answer this question, we need to substitute the value of 9 into the quadratic function as follows:
[tex]f(9)=-(9)^2+9+13=-81+22\Rightarrow f(9)=-59[/tex]Therefore, the answer is f(9) = -59.
5. What is the sum of 3 5/24, 6 7/24, and 9 9/24?,A. 14²/3B. 14 1/8C. 18 7/8D. 13 1/2
Answers
To answer this question, we can realize that we have mixed fractions. Then we need to add integers and fractions separately as follows:
1. We have:
[tex]3\frac{5}{24}+6\frac{7}{24}+9\frac{9}{24}[/tex]2. And this expression is equivalent to:
[tex]3+\frac{5}{24}+6+\frac{7}{24}+9+\frac{9}{24}[/tex]3. Now, we can add the integer parts, and the fractional parts separately as follows:
[tex](3+6+9)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})[/tex]4. Therefore:
[tex]18+\frac{5+7+9}{24}=18+\frac{21}{24}[/tex]5. We finally need to simplify the fraction, and then we will have:
[tex]\begin{gathered} \frac{21}{24}=\frac{\frac{21}{3}}{\frac{24}{3}}=\frac{7}{8} \\ 18+\frac{7}{8}=18\frac{7}{8} \end{gathered}[/tex]In summary, therefore, we have that the sum of the above fractions is:
[tex]18\frac{7}{8}[/tex][Option C.]
find the probability of obtaining five heads when flipping five coins. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answers
1/32
Explanation:In an experiment, we can only get head or tail:
Probability of getting a head = 1/2
Probability of obtaining five heads when flipping five coins:
[tex]\begin{gathered} \text{Probability = (1/2)}^{number\text{ of flips}} \\ \text{Probability = (1/2)}^5 \\ \end{gathered}[/tex][tex]\text{Probability = 1/32}[/tex](b) A company has 39 salespeople. A boardmember at the company asks for a list of the topsalespeople, ranked in order of effectiveness. How many such rankings are possible?0ExplanationCheck
Answers
Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.
[tex]39C4=\frac{39!}{4!(39-4)!}[/tex]Simplify the expression,
[tex]39C4=\frac{39!}{4!35!}[/tex][tex]\begin{gathered} 39C4=\frac{39\ast38\ast37\ast36}{4\ast3\ast2\ast1} \\ 39C4=\frac{1974024}{24} \\ 39C4=82251 \end{gathered}[/tex]answer:
The 4 top list can be arranged in 82251 ways
Perform the indicated operation 2 3/4-(-1 1/2) show all the work and give your answer as a fraction
Answers
2 3/4-(-1 1/2)=
2 3/4 + 1 1/2=
(2+1) (3/4 + 1/2)=
3 + 5/4=
3 + 1 1/4=
4 + 1/4=
4 1/4 or 17/4 or 4.25
13. You have $19.50 to buy subs for a party. Each sub costs $5.10. Estimate how many subs you can buy. Is your estimate too little or too much?
Answers
Let N be the number of subs, then we can write the following relationship:
[tex]5.10\cdot N=19.5[/tex]That is, this equality gives us the number of subs we can buy. If we move 5.10 to the right hand side, we have
[tex]\begin{gathered} N=\frac{19.50}{5.10} \\ N=3.82 \end{gathered}[/tex]this means that we can buy 4 subs approximately.
Express the number in scientific notation 6,340,000,000
Answers
Solution:
The number is given below as
[tex]6,340,000,000[/tex]Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form
Concept:
count the number from the last number and then stop in front of the first number 6 and then multiply in powers of 10
The general form of a scientific notation is given below as
By applying the concept, we will have
[tex]\begin{gathered} 6,340,000,000=6.34\times1,000,000,000 \\ 6,340,000,000=6.34\times10^9 \end{gathered}[/tex]Hence,
The final answer is
[tex]6.34\times10^9[/tex]Solve 7sin(pi/6 * x) = 2 for the four smallest positive solutions
Answers
Answer:
x =0.55, 5.45, 12.55, 17.45
Explanation:
First, we divide both sides by 7. This gives
[tex]\sin(\frac{\pi}{6}x)=\frac{2}{7}[/tex]then taking the inverse sine of both sides gives
[tex]\frac{\pi}{6}x=2\pi n\pm\sin^{-1}[\frac{2}{7}][/tex]since
[tex]\sin^{-1}[\frac{2}{7}]=16.60[/tex]Therefore,
[tex]\frac{\pi}{6}x=2\pi n\pm16.60[/tex]Multpilying both sides by 6/π
[tex][/tex]what is the best estimate for the value of the expression? [tex] ( \frac{34}{8} - \frac{16}{3}) - \frac{14}{9} [/tex]A. -3B.[tex] - 2 \frac{1}{2} [/tex]C. 7D. [tex]7 \frac{1}{2} [/tex]
Answers
-95/34
Explanation:
[tex](\frac{34}{8}-\frac{16}{3})-\frac{14}{9}[/tex]Simplify the expresssion:
[tex]\begin{gathered} \text{LCM for the one in the bracket is 24} \\ \frac{34(3)-8(16)}{24}-\frac{14}{9} \\ \frac{102-128}{24}-\frac{14}{9} \\ =\text{ }\frac{-26}{24}-\frac{14}{9} \end{gathered}[/tex][tex]\begin{gathered} \frac{-26(3)\text{ -14(8)}}{72} \\ =\text{ }\frac{-78-112}{72}=\text{ }\frac{-190}{72} \\ =\frac{-95}{36} \end{gathered}[/tex]None of the options has this value.
There is likely an error in question.
(10) When using substitution to solve this system of equations, what is the result of the first step? Eq#1 y = 6x + 3 Eq#2 x + 2y = 5
Answers
Given data:
The first equation given is y = 6x + 3.
The second equation given is x + 2y = 5.
Subsitute (6x+3) for y in second equation.
[tex]x+2(6x+3)=5[/tex]Thus, the first option is correct.
HiI’m bad at math I decided to practice but get confused Not is not assignment
Answers
Solution
Name an acute angle for which each of the angles are associated in terms of trig ratios:
Trigonometry ratios include sine, cosine and tangent
The associated angles interms of relation to acute angle is which of them is equivalent
[tex]sin150=sin30[/tex][tex]tan225=tan45[/tex][tex]cos300=cos60[/tex]Eugenia rolls a six-sided number cube. What is the probability that she gets anumber greater than 4?
Answers
A cube is six sided. The numbers which are greater than 4 in a cube are 5 and 6. So, there are two sides on the cube which has numbers greater than 4.
Hence, the number of desired outcomes, N=2.
Since the cube is six sided, the total number of outcomes, T=6.
So, the probability of getting a number greater than 4 while rolling a cube is,
[tex]P=\frac{N}{T}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the probability of getting a number greater than 4 is 1/3.
Option B is correct.
I need help with this practice problem Having a tough time completing step by step
Answers
we have the expression
[tex]\frac{cos(sin^{-1}(\frac{1}{2}))}{tan(cos^{-1}(-\frac{1}{2}))}[/tex]step 1
Find out the value of sin^-1 (1/2) and cos^-1(-1/2)
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=30^o \\ cos^{-1}(-\frac{1}{2})=120^0 \end{gathered}[/tex]substitute in the original expression
[tex]\frac{cos(30^o)}{tan(120^o)}=-\frac{1}{2}[/tex]Therefore
The answer is -1/2+ Type a messageSend2Help Mark use completing the square with the algebra tiles to convert this standard form equation to vertexform. Draw the tiles using this method and show the algebraic steps that take you from this equation to itsequivalent vertex form. Then state the vertex.014Show Your WorkCorrect answer y=xThis assignment has been submitted and is no longer editable.Client time: 5/13/2021, 6:06:10 PM (America/Los_Angeles)Server time: 5/13/2021, 6:06:10 PM (-70.44)Missing.omeos StommKB
Answers
From the image.
we have
1 y
1 x^2
6 x
8 (1squares)
We can write the standard equation as
[tex]y=x^{2^{}}+\text{ 6x +8}[/tex]But we need to express it in vertex form y = a(x-h)^2 + k where (h,k) is the vertex
to complete the squares we need to express the equation as
y = (x^2+6x+8+__)-___
to complete the square we need to add +1 inside the parenthesis and -1 outside
y = (x^2+6x+8+1)-1
We can express the equation
y = (x+3)^2 -1
[tex]y=(x+3)^2-1[/tex]Hi I just need a quick and easy explanation for this question I’m having a bit of trouble
Answers
Using the properties of parallel lines and transversal we can calculate the value of ∠5 as 64° .
The two lines are parallel to one another and the intersecting line is the transversal to the parallel lines.
the two given angles whose values are given are
∠4 = 106-y
∠6 = 3y-10
Now we can clearly see that these two angles ∠4 and ∠6 are co-interior angles.
We know that co-interior angles are supplementary.
Hence ∠4 + ∠6 = 180°
now we will put the values in the equation:
or , 106-y + 3y-10 = 180 °
or , 96 + 2y = 180 °
or, 2y = 84 °
or, y = 42°
Therefore ∠4 = 106 - y = 106° - 42° = 64°
Now from the properties of parallel lines we can see that ∠4 and ∠5 are alternate angles.
Hence ∠4 = ∠5 = 64°
therefore the value of ∠5 is 64° .
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CWhich of the following is the inverse of F(x)=2x+3?COAa 4520-19B.0 с.OD.103765PREVIOUSG Search or type URI(3,0)(15,0)3YSUBMIT
Answers
We have to find the inverse of the function f(x) = 2x + 3.
We can find the inverse function as:
[tex]\begin{gathered} f(f^{-1}(x))=x \\ 2f^{-1}(x)+3=x \\ 2f^{-1}(x)=x-3 \\ f^{-1}(x)=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]From the options we can see that the slope has to be positive, so we can discard optiosn B and C.
Then, we can check option A:
- It has a y-intercept of -1.5, which is equal to -3/2.
- The x-intercept is (3,0), what indicates that it increases 0.5 units of y per unit increase in x. This corresponds to a slope of 0.5 or 1/2.
Then, as both characteristics match with the equation of the inverse, the right representation is option A.
Answer:
The inverse is f^-1(x) = 1/2*x - 3/2 [Option A]
wich statement explain how Andy could prove what kind of quadrilateral this is ?
Answers
The first step is to locate the points to find what kind of quadrilateral this is.
The next step is to find the lengths of the diagonals, if both have the same length then the quadrilateral is a rectangle, if the don't the quadrilateral is a parallelogram.
When looking at the picture is easy to determine that the quadrilateral is a parallelogram, but the statement that could prove what kind of quadrilateral this is is C. Find the lengths of the diagonals to show that the quadrilateral is a parallelogram.
Find the equation of the axis symmetry:Find the x-intercept(s):and y-intercept(s):Find the coordinates of the vertex:
Answers
Step 1
Find the equation of the axis of symmetry
[tex]\begin{gathered} From\text{ the graph the zeroes are} \\ x=-2 \\ \text{and} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence the function is } \\ y=(x+2)(x-4) \\ y=x^2-4x+2x-8 \\ y=x^2-2x-8 \end{gathered}[/tex]The equation of symmetry is given as
[tex]\begin{gathered} x=\frac{-b}{2a} \\ b=-2 \\ a=1 \\ c=-8 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-2)}{2(1)} \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]Step 2
Find the x-intercepts
[tex]\begin{gathered} \text{From the graph, the x-intercepts are}; \\ (4,0),(-2,0) \end{gathered}[/tex]Step 3
Find the y-intercepts
[tex]y\text{-intercept; (0,-8)}[/tex]Step 4
Find the coordinates of the vertex
[tex]The\text{ coordinates of the Vertex ; (1,-9)}[/tex]A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid.
Answers
Given
A function moves around a circle
Find
Is the function sinusoidal
Explanation
Final Answer
Yes, the function is sinusoidal
?What is the factored form of x6 - 9?O(x + 3)(x – 3)(x5 + 3)(x – 3)o(x3 + 3)(x2 - 3)o(x3 + 3)(x3 - 3)+DONE
Answers
Answer:
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]Explanation:
Given the expression
[tex]x^6-9[/tex]It can be rewritten as
[tex]x^{2\cdot3}-3^2=\lparen x^3)^2-3^2[/tex]Use the formula
[tex]a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]to get
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]which is the factored form of the given expression.
Answer:
It's Option D
Step-by-step explanation:
edge