the fraction 1/5 horizontally expands the graph and the constant 12 move up the graph because is a sum
so the right option is the last
D. The graph of f(x) is vertically compressed by a factor of 5 and
shifted 12 units up
At a cost of s stickers for c cents, how many stickers can be bought for d dollars
First, we need to express the amount of dollars d as cents, we can do this as we know that one dollar equals 100 cents, then d in cents would be:
[tex]d(\text{cents)}=d\times100cents[/tex]And from the statement of the question, we know that s stickers cost c cents, we can express that cost per sticker like this:
[tex]\frac{s\text{ stickers}}{c\text{ cents}}[/tex]And if we want to find the amount of stickers that we can buy, we just have to multiply d in cents by the cost per sticker, like this:
[tex]\text{number of sticker we can buy}=\frac{s\times d\times100}{c}[/tex]Distribute [tex]( - 5a + 2a {}^2 - 2)(2a - 4)[/tex]distribute
The given expression is
[tex](-5a+2a^2\text{ - 2)(2a - 4)}[/tex]To distribute, we would multiply the terms in each bracket individually and add or subtract where necessary. It becomes
[tex]\begin{gathered} -\text{ 5a}\times2a\text{ + (-5a}\times-4)+(2a^2\times2a)+(2a^2\times-4)+(-2\times2a)+(-2\times-4) \\ -10a^2+20a+4a^3-8a^2-4a+8 \\ 4a^3-10a^2-8a^2+20a-4a+8 \\ 4a^3-18a^2+16a\text{ + 8} \end{gathered}[/tex]Find each value or measure. Assume that all segments that appear to be tangentare tangent. Find JLK
Answer
Angle JLK = 31°
Explanation
To answer this, we will use the tangent-chord theorem.
So, the intercepted arc JNL has an angle 298°
Then, we can solve for the tangent chord angle next to it, Angle JLM first by saying
Angle JLM = (Intercepted arc JNL)/2
Angle JLM = (298°/2)
Angle JLM = 149°
Then, we can see that Angle JLM and Angle JLK lie on the same straight line, KLM.
Sum of angles on a straight line is 180°.
Angle JLK + Angle JLM = 180°
Angle JLK + 149° = 180°
Angle JLK = 180° - 149°
Angle JLK = 31°
Hope this Helps!!!
Find the value of the expression. 07-2 . (131 alw The value is I I
A project on Kickstarter for an iPad stylus raised 1,130% of their goal, raising a total of $322,507 from 7,457 supporters. What was their original goal?
Let:
x = Original goal
y = Final goal = $322507
a = Percentage raised = 1.130% = 0.0113
so:
[tex]\begin{gathered} y=x+ax \\ so\colon \\ y=x(1+a) \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{y}{1+a} \\ x=\frac{322507}{0.0113+1} \\ x=\frac{322507}{1.0113} \\ x=318903.3917 \\ x\approx318903.39 \end{gathered}[/tex]Answer:
The original goal was approximately $318903.39
In the diagram above <3 = 135 degrees find the measure of <4
First, let's draw the picture and write some information that we already know about it
Remember that a line that passes throw two parallel lines will make the same angles, so if we already know that the angle <3=135º (which is alpha in the draw) we can find the supplementary angle which is <4 (the angle that we want to know), lets do it:
Finally, the angle <4=45º
Solve f(x)= x^4 - 3x^2 + 2 using the radical root theorem and synthetic division.
Convert the following: 253 mm to m. ANS. _______ m
253mm is read 253 Millimeter.
'Milli" is a sub-multiple that has a value of:
[tex]10^{-3}[/tex]Thus, 253mm is
[tex]253\times10^{-3}m[/tex]Expressing this in standard form, it becomes:
[tex]2.53\times10^{-1}m[/tex]To Decimal places, it is;
[tex]0.253[/tex]Which expression is equivalent to 20 — 3(x + 2)?A 3X+ 14B —3x + 14 C -9x + 21 D 17x— 34
We have to simplify the expression:
[tex]20-3(x+2)[/tex]and see which expression is equivalent.
We can do it like this:
[tex]\begin{gathered} 20-3(x+2) \\ 20-3\cdot x-3\cdot2 \\ 20-3x-6 \\ 20-6-3x \\ 14-3x \\ -3x+14 \end{gathered}[/tex]This expression is equivalent to -3x+14.
Answer: -3x+14 [Option B]
Answer:
first option
Step-by-step explanation:
[tex]\frac{\frac{-2}{x}+\frac{5}{y} }{\frac{3}{y}-\frac{2}{x} }[/tex] ← combine fractions on numerator and denominator
= [tex]\frac{\frac{-2y+5x}{xy} }{\frac{3x-2y}{xy} }[/tex]
leave numerator, change division to multiplication and turn denominator 'upside down'
= [tex]\frac{-2y+5x}{xy}[/tex] × [tex]\frac{xy}{3x-2y}[/tex] ← cancel xy on numerator/ denominator
= [tex]\frac{-2y+5x}{1}[/tex] × [tex]\frac{1}{3x-2y}[/tex]
= [tex]\frac{-2y+5x}{3x-2y}[/tex]
Jan makes four claims about the twopolynomials Any 6x + 1 and 2x. The claims arelisted belowClaim 1 states that when 2x is added to 4xy + 5x +1 the sum is a polynomial.Claim 2 states that when 2x is subtractedfrom xy + 6x + 1 the difference is a polynomial.Claim 3 states that when 4xy + 5x + 1 is multipliedby 2x the product is a polynomial.Claim 4 states that when xy + 6x + 1 is divided by2x the quotient is a polynomialSelect all claims by Jan that are correct.
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division but is never division by a variable.
Therefore claim 4 is false.
When 2x is added, the resultant will be a polynomial.
when 2x is subtracted, the resultant will be a polynomial.
When multiplied by 2x also, the resutant will be a polynomial.
Solve for x.
√x+3 = 2√x-1
Answer:
x = 16
Step-by-step explanation:
sqrt x + 3 = 2 sqrt x - 1 subtract sqrt x from both sides
3 = sqrt x -1 add 1 to both sides
4 = sqrt x square both sides
16 = x
Between 10 P.M and 7:20 A.M., the water level in a swimming pool decreased by 7/12 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour? PLEASE HELP I DONT GET THIS AT ALL!
Answer:
0.0625 or [tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Interpreting the ProblemIf the water level decreases at a constant rate, then that just means that the relationship between the water level and time is linear or is a straight line if graphed.
Calculating Constant Rate:let's just say that: [tex]C = \text{ contant rate the water level dropped at each hour}[/tex]
this means if we added C by how many hours passed, we should get the amount the water level dropped: [tex]C+C+C+C\text{...how many hours passed} =\frac{7}{12}[/tex]
let's also just say that: [tex]H = \text{ amount of hours that passed}[/tex]
from here we can rewrite the equation using multiplication: [tex]CH = \frac{7}{12}[/tex]
we can now divide both sides to isolate C: [tex]C = \frac{\frac{7}{12}}{H}[/tex], so now all we have to do is find how many hours passed.
From 10 P.M to 12 A.M, 2 hours pass. From 12 A.M to 7 A.M, 7 hours pass and from 7 A.M to 7:20 A.M, 20 minutes pass
So we have: [tex]2 \text{ hours} + 7 \text{ hours} + 20 \text{ minutes} = 9\text{ hours} + 20\text{ minutes}[/tex]
We want to represent this as one value and also in hours, so we'll need to convert the minutes to hours. To see how many 20 minutes is to one hour, we simply divide this 20 minutes by how many minutes are in an hour, which is 60 minutes: [tex]\frac{20}{60} = \frac{1}{3}[/tex]
It's actually super useful to keep this in fraction form, and even convert the 9 hours to fraction form: [tex]9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3}[/tex]
Now from here, we know that: [tex]H = \frac{28}{3}[/tex]
so let's plug this into the expression we made! [tex]C = \frac{\frac{7}{12}}{\frac{28}{3}}\implies \frac{7}{12} * \frac{3}{28}[/tex]
before multiplying, we can rewrite 12 as (4 * 3) so we can cancel out the 3 in the numerator and denominator making the simplification process a bit easier. We can also rewrite 28 as (4 * 7) to cancel out the 7 in the numerator and denominator: [tex]C = \frac{7 * 3}{(4 * 3) * (7 * 4)} = \frac{1}{16} = 0.0625[/tex]
This means if we multiplied the 1/16 or 0.0625 by the 9.33333 hours that passed we would get the total amount that decreased: 7/12
Maybeline is the teacher's assistant today and is correcting homework examples. Help her by selecting correct or incorrect after evaluating each problem.
Here, we need to remember the signs rules
[tex]\begin{gathered} (+)(+\text{ )=+} \\ (+\text{ )(- )=-} \\ (-\text{ )(+ )=-} \\ (-\text{ )(- )=+} \end{gathered}[/tex]Then
[tex](-4)+(-8)=-4-8=-12[/tex]incorrect.
[tex](-9)-(-8)=-9+8=-1[/tex]correct
[tex](+7)\times(-8)=-56[/tex]correct
[tex](-5)(-2.5)=12.5[/tex]correct
[tex]+\frac{1}{2}\times(+6)=3[/tex]incorrect
Sanya's car can drive 300 miles in 6 hours. How many miles can she drive in 14 hours?
Assuming that these variables behave proportionally, we can solve this problem through proportional relationships:
[tex]\begin{gathered} \frac{300}{6}=\frac{x}{14} \\ x=\frac{300\times14}{6} \\ x=\frac{4200}{6} \\ x=700 \end{gathered}[/tex]She can drive 700 miles in 14 hours
Given this super-sized board (16x16), what integer lengths are possible for slanted segments? Use the line tool to sketch them (using a different color for each one). Label each length. Then describe how you found them.
A way to find integer line segments is using Pythagorean triples, that is, positive integers that are consistent with the Pythagorean theorem, for example, (3,4,5) because we have
[tex]3^{2^{}}+4^2=5^{2^{}}[/tex]therefore, they can be put in a triangle like this
Therefore, the slanted segment would have a length of 5. That can be done with other Pythagorian triples like (5,12,13) or (8,15,17).
The ages of grandparents of students in Mr. Keyes' third period class are listed below.52 54 57 61 56 6167 64 63 57 60 50A. Create the five-number summary that represents the data set.B. Create a box plot that represents the data set.
Given the data set (ages of grandparents):
52, 54, 57, 61, 56, 61, 67, 64, 63, 57, 60, 50
Let's create a five-number summary that represents the given data set and also create a box plot.
A) A five number summary of a data set consists of the following:
• Minimum value
,• First quartile
,• Median
,• Third quartile
,• Maximum value
Let's determine the five-number summary of the given data set.
• Minimum value:
The minimum value is the smallest number from the given data set.
Thus, the minimum is = 50
• First quartile:
The first quartile is also called the lower quartile. It is the median of the lower half of the data set.
To find the first quartile, list out the lower half of the data set after arranging the data in acsending order.
Arrange in ascending order: 50, 52, 54, 56, 57, 57, 60, 61, 61, 63, 64, 67
Lower half: 50, 52, 54, 56, 57, 57
Median of lower half:
[tex]\frac{54+56}{6}=\frac{110}{2}=55[/tex]Therefore, the first quartile is = 55
• Median:
Median is the middle term of the data set.
50, 52, 54, 56, 57, 57, 60, 61, 61, 63, 64, 67
The middle terms are = 57 and 60
To find the median, divide the sum of the middle terms by 2.
Thus, we have:
[tex]\frac{57+60}{2}=\frac{117}{2}=58.5[/tex]Therefore, the median of the data set is 58.5
• Third Quartile:
The third quartile is also called the upper quartile. It is the median of the upper half of the data set.
Upper half of data set = 60, 61, 61, 63, 64, 67
Median of upper half =
[tex]\frac{61+63}{2}=\frac{124}{2}=62[/tex]Therefore, the third quartile is 62
• Maximum value:
The maximum value is the greatest number in the given data set.
The greatest number in the data set is 67.
Therefore, the maximum value is 67.
We have the five-number summary that represents the data set below:
• Minimum = 50
,• First quartile = 55
,• Median = 58.5
,• Third quartile = 62
,• Maximum = 67
b) Let's create a box plot that represents the data set.
We have the box plot below:
Use the graph of f to find the value of f(0)
Solution:
The expression f(0) represents the y-intercept on the graph of f(x). The y-intercept of a graph is the point where the graph crosses the y-axis.
Thus, from the graph;
[tex]f(0)=0[/tex]Savannah invested $5,300 in an account paying an interest rate of 3 5/8 % compounded daily.
The amount that will be in Savannah's account after 3 years is $6042.
What is compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
To calculate the amount that will be in Savannah's account after 3 years, we use the formula below.
Fromula:
A = P(1+R/365)³⁶⁵ⁿ........... Equation 1Where:
A = Amount P = PrincipleR = Raten = time/yearsFrom the question,
Given:
P = %5300R = 35/8% = 4.375% = 0.04375n = 3 yearsSubstitute these values into equation 1
A = 5300(1+0.04375/365)³ˣ³⁶⁵A = 5300(1.00012)¹⁰⁹⁵A = 5300×1.14A = $6042Hence, there would be $6042 in the account.
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Compelete question: Savannah invested $5,300 in an account paying an interest rate of 3 5/8 % compounded daily, Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 3 years?
12. Given that a || b, what is the value of x? (The fiş290ToI41°5
Ok, so
Here we have the following figure:
We know that both segments are parallel and we want to find the value of x.
For this, remember that the value of x will be the sum of the other two angles:
[tex]\begin{gathered} x=29+41 \\ x=70 \end{gathered}[/tex]This is:
Given the following figure:
The value of x can be find using the following equation:
[tex]x=a+b[/tex]One more question please ?
The total bill for repairing Mark’s TV was $211. The repair shop charges $25 an hour for labor plus $16 for parts. How many hours of labor did it take to repair Mark’s TV? Write it in an equation.25/16x = 21125 - 16x = 21125x – 16 =21125x + 16 = 211
Solution:
Given the total, T is $211;
One hour of labor is $25. So, x hours is $25x
Then, the cost of parts is $16.
Thus;
[tex]25x+16=211[/tex]Find the equation of the line that is parallel to Y = x -3 and contains the point (3,-2)
Given:
The equation of the line is
[tex]y=x-3[/tex]Required:
Find the equation of the line that is parallel to the given line and contains the point (3,-2).
Explanation:
The given equation of the line is
[tex]y=x-3[/tex]Compare the equation with the equation
[tex]y=mx+c[/tex]The slope of the line m = 1.
Since the slope of the parallel lines is equal.
The equation of the line that is parallel to the given line is:
[tex]y=x+b[/tex]This line contains the point (3,-2).
[tex]\begin{gathered} -2=3+b \\ b=-5 \end{gathered}[/tex]Thus the equation of the parallel line is:
[tex]y=x-5[/tex]Final Answer:
[tex][/tex]Let f(x) = 4x^3-5x^2Then f(x) has a local minimum at x= ____a local maximum at x= ____and inflection point at x= ____ write inflection points (if any) in numerical order smallest first
Given:
[tex]f\mleft(x\mright)=4x^3-5x^2[/tex]Find-: Local minimum and local maximum and inflection point.
Sol:
Derivative of function.
[tex]\begin{gathered} f\mleft(x\mright)=4x^3-5x^2 \\ f^{\prime}\left(x\right)=12x^2-10x \\ f^{\prime}\left(x\right)=2x\left(6x-5\right) \end{gathered}[/tex]The critical point is:
[tex]\begin{gathered} f^{\prime}\left(x\right)=0 \\ 2x\left(6x-5\right)=0 \\ 2x=0;6x-5=0 \\ x=0;x=\frac{5}{6} \end{gathered}[/tex]Local minima is:
[tex]\left(x,f\lparen x\right))=\lparen\frac{5}{6},-1.157)[/tex]Local minima at x=5/6
Local maxima at x=0
Inflection point.
[tex]\begin{gathered} f=4x^3-5x^2 \\ \text{ Inflection point} \\ x=\frac{5}{12} \end{gathered}[/tex]an elevation on the tenth floor goes down 9 floors then it goes up 19 floors down three and finally down 12 what floor does it end up on write an equation to show how you found your answer
onIn order to solve this, we have to add the number of floors the elevator goes up and subtract the number of floors the elevator goes down, like this:
Initially, it goes down 9 floors since it was at the 10th floor we get:
10 - 9 = 1
Then, after it goes down 9 floors it gets to the first floor, then it goes up 19 floors , now we get:
1 + 19 = 20
After it goes up to the 19th floor from the fits one, it gets to the 20th floor, then it goes down 3 floors, now we get:
20 - 3 = 17
After it goes down 3 floors it gets to the 17th floor, then it goes 12 floors down from the 17th floor:
17 - 12 = 15
At the end, the elevator ends up in the 15th floor
Last year, Lisa opened an investment account with $8400. At the end of the year, the amount in the account had decreased by 24.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?
Answer:
The dec
Explanation:
Given that Lisa opened an investment account with $8400, at the end of the year, the amount in the account had decreased by 24.5%. We want to know how much the decrease is, and how much was in her account at the end of last year.
All we are required to find is what value is 24.5% of $8400
24.5% is the same as:
[tex]\frac{24.5}{100}[/tex]24.5% of $8400 is now:
[tex]\begin{gathered} \frac{24.5}{100}\times8400 \\ \\ =24.5\times84 \\ =2058 \end{gathered}[/tex]Therefore 24.5% of $8400 is $2058
This amount is the decrease.
Finally, at the end of last year, the amount in her account is:
$8400 - $2058 = $6342
Answer: If you do 8400 - 24.5% you get 6342. Then if you do 8400 - 6342 you get 2058. So her account decreased by $2,058 and she had $6342 left in her account at the end of the year.
Determine the slope (m) and y-intercept (b) of the line:y = 2x - 3A) m = 3, b = 2B) m = 2, b = -3C) m = -3, b = 2D) m = 2, b = 3
slope of line(m) = 2 and intercept on y axis is -2 that is 2 unit in negative y axis.
Equation of line in slope intercept form:
Slope:
Slope is known as tangent of an angle made by positive X-axis.
We know equation of line in slope and intercept form is,
y = mx + b
where,
m is slope of line
b is intercept on y axis
hence for the given equation,
y =2x - 3
slope (m) will be = 2
intercept on y axis (b) = -3
thus,
option (B) will be correct.
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Determine the length of the longest side of the triangle ABC. Showyour work and round answers to the nearest tenth. *15 in.CB78°10 in.A
We would make use of the cosine rule,
[tex]\begin{gathered} C^2=A^2+B^2-2AB\cos C \\ C^2=15^2+10^2-2\times10\times15\times\cos 78 \end{gathered}[/tex][tex]\begin{gathered} C^2=325-62.374\text{ =262.626} \\ C=\text{ 16.206 }\approx\text{ 16.2 in} \end{gathered}[/tex]Find the missing length of the triangle. 14 cm 8.4 cm b The missing length is centimeters.
Answer:
11.2cm
Explanation:
To be able to determine the missing length, we have to apply the Pythagorean Theorem which states that, in a right-angled triangle, the square of the hypotenuse(the longest side) is equal to the sum of squares of the other two sides.
Let's go ahead and find b as follows;
[tex]\begin{gathered} 14^2=8.4^2+b^2 \\ 196=70.56+b^2 \\ 196-70.56=b^2 \\ 125.44=b^2 \\ b=\sqrt[]{125.44}=11.2\operatorname{cm} \end{gathered}[/tex]Write a variation equation for the following situation. Use k as the constant of variation.R varies inversely as the square of h.The variation equation is ______
Given
R varies inversely as the square of h
Find
Equation for the given statement
Explanation
[tex]\begin{gathered} R\propto\frac{1}{h^2} \\ \\ R=\frac{k}{h^2} \end{gathered}[/tex]Final Answer
The equation for given statement is
[tex]R=\frac{k}{h^2}[/tex]What is the axis of symmetry for f(x) = x2 + 4x + 6? A. x= -4B. X= -2C. X = 2D X = 3
Answer:
Step by step explanation:
In order to find the axis of symmetry, we will have to find the x-value of the vertex
[tex]\text{Vertex = }\lbrack\frac{-b}{2a},\text{ f(}\frac{-b}{2a})\rbrack[/tex][tex]x^2\text{ + 4x +6}[/tex]a = 1
b = 4
c = 6
[tex]\text{Vertex = }\lbrack\frac{-4}{2},f(\frac{-4}{2})\rbrack[/tex][tex]Vertex=\lbrack-2,f(-2)\rbrack\text{ }[/tex]We have found the x-value of the vertex which is -2
Line/axis of symmetry is x=-2