Answers
Given sentence:
Five more than half the input is the output
y is the output, x is the input
To interpret the sentence, we should break it into parts:
-half the input: we half the input
- 5 more than we add 5 to the new input
- the sum of these is the output
The equation that represents the given sentence:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]Answer:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]Related Questions
Estimate the instantaneous rate of change of the function f(x)=x2−2x+1 at x=−1 using the average rate of change over successively smaller intervals.
Answers
The instantaneous rate of change of the function f(x)=x²−2x+1 at x=−1 using the average rate of change over successively smaller intervals is 4.
What is function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input.
Here,
x²-2x+1
x=-1
(-1)²-2*-1+1
1+2+1=4
the instantaneous rate of change=4
Using the average rate of change over successively smaller intervals, the instantaneous rate of change of the function f(x)=x²-2x+1 at x=1 is 4.
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10Ana wants to multiply out the brackets in the expression 2(3a-1).She writes 2(3a-1)=6a - 1.Ana is wrong. Explain why.1Show Your WorkYou have responded to 9 of 10 questions
Answers
Answer:
[tex]2(3a-1)=6a-2[/tex]Step by step explanation:
To multiply the expression 2(3a-1), we need to use the distributive property of multiplication which states that:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]Then, for the expression 2(3a-1), the correct answer would be:
[tex]\begin{gathered} 2(3a-1)=2\cdot3a-2\cdot1 \\ 2(3a-1)=6a-2 \end{gathered}[/tex]Five CDs cost $80 . If each CD costs the same, how much does one cost
Answers
solution:
5 CDs ----> $80
1 CDs ----> x
then
[tex]x=\frac{80}{5}=16[/tex]answer: one CD cost $16
True or false: Are vertical angles only congruent if they are marked, and why ?
Answers
The vertical angles formed when two lines intersected each other at a point
The vertical angles are always equal in mesuaresSorry
So you do not want a mark to know they are equal
The answer is false
To solve rational equation shown below, find the common denominator
Answers
Given:
[tex]\frac{3}{2x+1}=\frac{5}{4x+3}[/tex][tex]3(4x+3)=5(2x+1)[/tex][tex]12x+9=10x+5[/tex][tex]12x-10x=5-9[/tex][tex]2x=-4[/tex][tex]x=-\frac{4}{2}[/tex][tex]x=-2[/tex]Is it always, sometimes, or never true that an equation in slope-intercept form represents a direct variation? Support your answer with examples
Answers
It is always true an equation in slope-intercept form represents a direct variation.
For example, the amount of money you earn by hours.
Let:
x = Number of hours
y = Amount of money
a = Money per hour = $5
The equation will be:
[tex]\begin{gathered} y=ax \\ y=5x \end{gathered}[/tex]Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Answers
Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Remember that
the area of the triangle is
[tex]A=\frac{1}{2}b\cdot h[/tex]we have
b=4 in
at least -----> is greater than or equal to
so
[tex]A\ge12\text{ in2}[/tex]therefore
[tex]\begin{gathered} \frac{1}{2}\cdot(4)\cdot h\ge12 \\ \text{solve for h} \\ 2h\ge12 \\ h\ge6\text{ in} \end{gathered}[/tex]the height of triangle must be greater than or equal to 6 inches
A guidebook says that one night at a mid-range hotel the capital city, republica cost between $25 an $40 us dollars. The hotel capital city offers a one week rental for 150 rp ( republica pounds) the current exchange rate is 1=0.0147 usd ($us dollars) does the price per night at the hotel capitol suggest that it a mid range hotel?
Answers
To determine if the hotel capital suggests is a mid-range hot, we need to do the conversion:
[tex]150rp\cdot\frac{0.0147\text{usd}}{1rp}=2.2\text{ usd}[/tex]By the exchange rate 1rp=0.0147usd, notice the rental week of Hotel Capital city is $2.2
Then, for the night:
[tex]\frac{2.2}{7}=0.31[/tex]Then, a night at Hotel Capital City would be $0.31. It is not a mid-range hotel.
Chauncey is studying a 250-mg sample of a radioasubstance has a half-life of 5 days. Write an equatsubstance, s, is left after n days?aS =b= 250 (3)s = 250 (3)s = 250 (0.5)s = 250 (0.5)$5nd
Answers
Answer:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]Step by step explanation:
Exponential functions are represented by the following expression:
[tex]\begin{gathered} f(x)=ab^x \\ \text{where,} \\ a=\text{initial amount} \\ b=\text{decay factor} \\ x=\text{time(days)} \end{gathered}[/tex]Then, for this situation, we have an initial amount of 250, a decay factor of (0.5) in 5 days:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]what is the area of a semicircle with a diameter of 2 ?
Answers
we have that
the area of semicircle is equal to
[tex]A=\frac{1}{2}\cdot\pi\cdot r^2[/tex]we have
r=2/2=1
substitute
[tex]\begin{gathered} A=\frac{1}{2}\cdot\pi\cdot1^2 \\ A=\frac{\pi}{2} \end{gathered}[/tex]area is equal to pi/2 square unitsRangers wanted to estimate the total number of elk in region of Montana. they tagged 12 elk and sent them back to the area. two months later the Rangers observed 4 of the tagged elk out of 25 total Elk observed. estimate the size of the elk population in that region of Montana
Answers
Total number of elks tagged = 12
Number of a sample of the tagged elks from 25 total Elk observed = 4
Total number of 25 Elk observed = 12/4 = 3
Size of the elk population in the region of Montana = 3 x 25
= 75
which word phrase represents the following expression n-3A) the quotient of n and 3B) 3 less than nC) n less than 3
Answers
Answer:
B) 3 less than n
Explanation:
Given the expression:
[tex]n-3[/tex]This means that the value of n is being reduced by 3.
Thus, the appropriate word phrase is: 3 less than n.
The correct choice is B.
A glass jar contains 3 red, 13 green, 4 blue, and 8 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a(a) red marble? (b) green marble? (c) blue marble?
Answers
Solution
(a) red marble?
[tex]p=\frac{\text{red}}{\text{total}}=\frac{3}{3+13+4+8}=\frac{3}{28}[/tex](b) green marble?
[tex]p=\frac{\text{gren}}{\text{total}}=\frac{13}{3+13+4+8}=\frac{13}{28}[/tex](c) blue marble?
[tex]p=\frac{\text{blue}}{\text{total}}=\frac{4}{3+13+4+8}=\frac{4}{28}[/tex]what is the ratio 250 pieces of red construction paper and 114 blue construction paper
Answers
Answer
Check Explanation
Explanation
We need to find the ratio of red construction paper to blue construction paper.
250 : 114
Divide both sides by 2
125 : 57
That's how far we can go, since there is no number that can divide these two numbers.
Hope this Helps!!!
Seth charges $42 for 2 hours of baseball lessons. Bennie charges $65 for 3 hours of baseball lessons. Who offers the better deal? Why?
Answers
Answer:
Seth offers the better deal, because his charge per hour is lower.
Explanation:
Given that;
Seth charges $42 for 2 hours of baseball lessons.
Seth's Charge rate per hour would be;
[tex]\begin{gathered} r_s=\frac{\text{ \$42}}{2\text{ hours}} \\ r_s=\text{ \$21 per hour} \end{gathered}[/tex]Also, Bennie charges $65 for 3 hours of baseball lessons.
[tex]\begin{gathered} r_b=\frac{\text{ \$65}}{3\text{ hours}} \\ r_b=\text{ \$21.67 per hour} \end{gathered}[/tex]From the given deals, the deal with the lower Charge rate per hour offers the better deal.
So, Seth offers the better deal, because his charge per hour is lower.
Which can be the first step in finding the equation of the line passing through (5,-4) and (-1,8)
Answers
The equation of the line, in slope-intercept form, is written as
[tex]y=mx+b[/tex]wherein m is the slope of the line and b is the y-intercept.
The first step to solve the equation of the line that passes through two points is to find the slope of the line given two points. The slope of the line can be computed using the equation
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For points (5, -4) and (-1, 8), the slope of the line is
[tex]m=\frac{8-(-4)}{-1-5}=\frac{12}{-6}=-2[/tex]Now, we have the initial equation of the line written as
[tex]y=-2x+b[/tex]To solve for the value of b, we use one of the points and substitute it on the initial equation above. In my case, I will be using points (5,-4), we have
[tex]\begin{gathered} -4=-2(5)+b \\ -4=-10+b_{} \\ b=10-4 \\ b=6 \end{gathered}[/tex]Hence, the equation of the line that passes through (5,-4) and (-1,8) is
[tex]y=-2x+6[/tex]#14 iW Ua. Give another name for UVb. Name a ray with endpoint Xc. Match each ray with its opposite ray.
Answers
Given
Find
a) another name for UV
b) Name a ray with endpoint X
c) Match each ray with its opposite ray.
Explanation
a) another name for UV is VU
b) ray with endpoint X is UX
c)
i) UZ is opposite to UY
ii) UV is opposite to UW
iii) UX is opposite to UT
Final Answer
Hence ,
a) VU
b) UX
c) UY , UW , UT
To start a new business Beth deposits $1500 at the end of each six-month period in an account that pays 8%, compounded semiannually. How much will she have at the end of 9 years?
Answers
The amount Beth deposit every six-month is A = $1500.
The rate percent is 8% or 0.08.
The time after which futre value determined is t = 9 years.
Determine the rate percent for semi-annually.
[tex]\begin{gathered} i=\frac{0.08}{2} \\ =0.04 \end{gathered}[/tex]Determine the value of time (t) for semi-annualy.
[tex]\begin{gathered} n=2\cdot9 \\ =18 \end{gathered}[/tex]The formula for the future value is,
[tex]FV=\frac{A}{i}\lbrack(1+i)^n-1\rbrack[/tex]Substitute the values in the formula to determine the future value.
[tex]\begin{gathered} FV=\frac{1500}{0.04}\lbrack(1+0.04)^{18}-1\rbrack \\ =37500\lbrack(1.04)^{18}-1\rbrack \\ =38468.11933 \\ =38468.12 \end{gathered}[/tex]So answer is 38468.12
A new car worth $27,000 is depreciating in value by $3,000 per year. After how many years will the car's value be $3,000?
Answers
The equation for the worth of car after x number of years is,
[tex]\begin{gathered} y=27000-3000\cdot x \\ =27000-3000x \end{gathered}[/tex]Substitute 3000 for y in the equation to obtain the value of x.
[tex]\begin{gathered} 3000=27000-3000x \\ 3000x=27000-3000 \\ x=\frac{24000}{3000} \\ =8 \end{gathered}[/tex]So after 8 years the worth of car is $3000.
Can someone help me with this question?
Answers
So the average decrease will be 50% for the season of 5 weeks as the definition of percent decrease will be "The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease".
What is percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease.
Here,
The percent decrease will be,
48000-24000=24000
24000/48000*100=50%
24000-12000=12000
12000/24000*100=50%
12000-6000=6000
6000/12000*100=50%
6000-3000=3000
3000/6000*100=50%
3000-1500=1500
1500/3000*100=50%
Due to the definition of percent decrease being a season of five weeks, the average decrease will be 50% "The percentage decrease is the difference between the starting and ending values. Regardless of the units, it shows a percentage decline in value relative to the starting point. The amount of decrease is the difference between the initial and final amounts ".
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The coach of a soccer team keeps many stats on her teams performance. For example, she records if the team was ahead, behind, or tired with the opponent at the end of each half.pic is the summary of the data she got after 60 games. Supposed the coach continue recording the end-of-half results for 80 more games. In how many of these 80 games will the team be tied at the end of neither half. Use the data to make a prediction
Answers
Given:
The stat of the team is given in the table.
Required:
We have to find in how many of 80 games will the team be tied at the end of neither half.
Explanation:
The total number of games given in the table is
[tex]4+8+12+3+6+9+5+4+9=60[/tex]The number of games in which the team has tied at the end of neither half is
[tex]4+8+3+6=21[/tex]Then the percentage of the team has tied at the end of neither half is
[tex]\frac{21}{60}\times100=0.35\times100=35\text{ \%}[/tex]Hence the number of games in which the team be tied at the end of neither half in those 80 games is
[tex]35\text{\% of }80=\frac{35}{100}\times80=0.35\times80=28[/tex]Final answer:
Hence the final answer is
[tex]28[/tex]Pamela's mother purchased five boxes of candy bars. If each box contains 20 bars, how many candy bars does Pamela's mother have? Explain your answer.
Answers
If each box contains 20 bars and Pamela's mother purchased 5 boxes
To get the number of candy bars Pamela's mother have, we will simply multiply the number of box by the number oc candy in each box
That is; 5 x 20bars = 100 candy bars
Hence Pamela's mother have 100 candy bars
Find a cofunction with the same value as the given expression.COS(3pi/7)
Answers
We will have the following:
[tex]\cos (\frac{3\pi}{7})=\sin (\frac{\pi}{2}-\frac{3\pi}{7})[/tex][tex]=\sin (\frac{\pi}{14})[/tex]So, the cofunction with the same value as the expression gu
solve the equation by completing the square.4x(x + 6) = -40
Answers
Answer:
The solution to the equation is;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]Explanation:
Given the equation below;
[tex]4x(x+6)=-40[/tex]Expanding the bracket we have;
[tex]4x^2+24x=-40[/tex]dividing through by 4;
[tex]\begin{gathered} \frac{4x^2}{4}+\frac{24}{4}x=-\frac{40}{4} \\ x^2+6x=-10 \end{gathered}[/tex]To solve by completing the square, let us add the square of half of 6 to both sides;
[tex]\begin{gathered} x^2+6x+(\frac{6}{2})^2=-10+(\frac{6}{2})^2 \\ x^2+6x+9=-10+9 \\ x^2+6x+9=-1 \\ (x+3)^2=-1 \end{gathered}[/tex]taking square roots of both sides;
[tex]\begin{gathered} x+3=\sqrt[]{-1} \\ x+3=\pm i \end{gathered}[/tex]So;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]Use the correct trigonometric function to solve for both x and y .
Answers
As per given by the question.
There are given that a triangle.
Now,
Suppose given triangle is ABC.
Then, redraw the given triangle.
Now,
For finding the value of x, and y;
First find the value of x with the help of sine trigonometric function.
So,
[tex]\sin 35^{\circ}=\frac{AB}{AC}[/tex]Then,
Substitute the value x for AB and 22 for AC.
SO,
[tex]\begin{gathered} \sin 35^{\circ}=\frac{AB}{AC} \\ \sin 35^{\circ}=\frac{x}{22} \\ 0.57=\frac{x}{22} \\ x=0.57\times22 \\ x=12.54 \end{gathered}[/tex]Now,
For finding the value of y,
Here, use pythagoras theorem in triangle ABC.
So, from the pythagoras theorem;
[tex]AB^2+BC^2=AC^2[/tex]Then,
Substitute the value in above formula;
So,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ x^2+y^2=(22)^2 \end{gathered}[/tex]Now, put the value 12.54 for x,
So,
[tex]\begin{gathered} x^2+y^2=(22)^2 \\ (12.54)^2+y^2=(22)^2 \\ 157.25+y^2=484 \\ y^2=484-157.25 \\ y^2=326.75 \end{gathered}[/tex]Then,
[tex]\begin{gathered} y^2=326.75 \\ y=\sqrt[]{326.75} \\ y=18.076 \end{gathered}[/tex]Hence, the value of x is 12.54 and the value of y is 18.076.
The endpoints of AB are A(9,4) and B(5,-4). The endpoints of its image after a dilation are A'(6,3) and B'(3,-3). Find the scale factor and explain each of your steps.
Answers
It is given that the line segment AB is dilated to give another line segment A'B'.
Since it is a dilation, the length of the image will be a multiple of the length of the preimage.
To find the scale factor, divide the length of the image by the length of the preimage.
Recall that the length of a line segment with endpoints (a,b) and (c,d) is given as:
[tex]\sqrt[]{(c-a)^2+(d-b)^2}[/tex]To find the length AB of the preimage, substitute the coordinates (a,b)=(9,4) and (c,d)=5,-4) into the formula:
[tex]AB=\sqrt[]{(5-9)^2+(-4-4)^2}=\sqrt[]{(-4)^2+(-8)^2}=\sqrt[]{16+64}=\sqrt[]{80}[/tex]To find the length A'B' of the image, substitute the coordinates (a,b)=(6,3) and (c,d)=(3,-3) into the formula:
[tex]A^{\prime}B^{\prime}=\sqrt[]{(3-6)^2+(-3-3)^2}=\sqrt[]{(-3)^2+(-6)^2}=\sqrt[]{9+36}=\sqrt[]{45}[/tex]Divide the length of the image by the length of the preimage to calculate the scale factor:
[tex]\frac{A^{\prime}B^{\prime}}{AB}=\frac{\sqrt[]{45}}{\sqrt[]{80}}=\sqrt[]{\frac{45}{80}}=\sqrt[]{\frac{9}{16}}=\frac{\sqrt[]{9}}{\sqrt[]{16}}=\frac{3}{4}[/tex]Hence, the scale factor is 3/4.
The answer is 3/4.
How large is the sample space when rolling a die five times?
Answers
7776
ExplanationThe size of the sample space is the total number of possible outcomes.for example, for a dice, the possible outcomes are 1, 2,3 4, 5 or 6, when rolling a dice five times we have:
Each time you roll the dice there are 6 possible outcomes. (1 of 6)
[tex]6[/tex]now, you have to roll the dice five times
then
[tex]\text{sample space=6}^5=6\cdot6\cdot6\cdot6\cdot6=7776[/tex]I hope this helps you
For each of the following, find the Lateral Area, Surface Area, and Volume. Leave answers in terms ofFt, and if applicable, round to the nearest tenth.1. TA =V=A sphere with radius of 21 cm.
Answers
Given a sphere with radius R, the volume and the surface area formulas are expressed as:
[tex]\begin{gathered} V=\frac{4}{3}\pi R³ \\ \\ A=4\pi R² \end{gathered}[/tex]Now, if we have a sphere of radius R = 21 cm = 0.688976 ft. Then, using the formulas:
For the volume
[tex]\begin{gathered} V=\frac{4}{3}\pi(0.688976)³ \\ \\ \therefore V=1.37\text{ ft^^b3} \end{gathered}[/tex]For the surface area
[tex]\begin{gathered} A=4\pi(0.688976)² \\ \\ \therefore A=5.97\text{ ft^^b2} \end{gathered}[/tex]Solve the system of linear equations by eliminations-- 3x + 4y = 186x+2y = -6does thia system have a solution?
Answers
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $200 and first-class seats for $940 Sheyee her total budget for airfare for the trip, which was $4220. How many first-class tickets did she buy? How many coach tickets did she buy? number of first-class tickets bought = number of coach tickets bought =
Answers
Answer:
• The number of first-class tickets bought = 3
,• The number of coach tickets bought =7
Explanation:
Let the number of first-class tickets bought = x
Let the number of coach tickets bought = y
A total of 10 people took the trip:
[tex]\implies x+y=10[/tex]Her total budget for the trip's airfare = $4220.
[tex]\implies200y+940x=4220[/tex]Next, solve the two equations simultaneously:
[tex]\begin{gathered} x+y=10\implies x=10-y \\ 940x+200y=4220 \end{gathered}[/tex]Substitute x into the second equation:
[tex]\begin{gathered} 940(10-y)+200y=4220 \\ 9400-940y+200y=4220 \\ 9400-740y=4220 \\ 9400-4220=740y \\ 5180=740y \\ \frac{5180}{740}=y \\ y=7 \end{gathered}[/tex]Recall: x=10-y
[tex]\begin{gathered} x=10-7 \\ x=3 \end{gathered}[/tex]Thus:
• The number of first-class tickets bought, x = 3
,• The number of coach tickets bought, y =7