Answers
Solution
We want to find the equation of the line given in the graph
We can see the four points on the graph where the line pass through
The points are
[tex](4,4),(2,3),(0,2),(-4,0)[/tex]We first obtain the slope (m)
The formula for finding the slope is given as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the points (0,2) and (-4,0) (indeed we can pick any two points, we will still obtain the same answer)
Here
[tex]\begin{gathered} x_1=0 \\ y_1=2 \\ x_2=-4 \\ y_2=0 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-2}{-4-0} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \\ m=0.5 \end{gathered}[/tex]We can use any of the points above to find the equation
Equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]Using (4,4)
[tex]y-4=0.5(x-4)[/tex]Option D is correct
Using (2,3)
Related Questions
Add the equation below:-9p=3p + 18Hint: We can isolate the variable by dividing each side by factors that don't contain the variable.
Answers
We have the next given equation:
[tex]9p=3p+18[/tex]Now, we can subtract both sides by 3p:
[tex]\begin{gathered} 9p-3p=3p-3p+18 \\ 6p=18 \end{gathered}[/tex]Then, divide both sides by 6:
[tex]\begin{gathered} \frac{6p}{6}=\frac{18}{6} \\ p=3 \end{gathered}[/tex]Hence, the answer is p=3
on one side of the balance scale, Henry placed gram weight. on the other side of the scale, he placed a ballet slipper. how many milligrams does the slipper weigh?
Answers
Solution
Step 1
Convert gram to milligram
1 gram = 1000 milligram
Step 2
Find the answer
Assuming it is 1 gram weight on one side of the balance scale then, the ballet slippers will weigh 1 gram for the scale to be balanced.
I gram = 1000 milligram
Hence the ballet slippers will weigh 1000 milligrams
Cheng-Yu ordered a book that cost $24 from an online store. Hertotal with the shipping charge was $27. What was the percent ofmarkup charged for shipping?
Answers
Given:
Cost of book = $24
Total cost of book (shipping charge inclusive) = $27
The shipping charge is:
Total cost - cost of book = $27 - $24 = $3
The shipping charge is $3
To find the percentage markup charged for shipping, use the formula:
[tex]\frac{ship\text{ charge}}{Total\text{ cost}}\ast100[/tex][tex]\frac{3}{27}\ast100\text{ = }0.111\text{ }\ast\text{ 100 = }11.1percent^{}[/tex]Therefore, the percent of markup charged for shipping is 11.1%
ANSWER:
11.1%
Mai must choose a number between 49 and 95 that is a multiple of 3, 8, and 12. Write all the numbers that she could choose. If there is more than one number, seperate them with commas.
Answers
Answer:
72
Explanation:
To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.
Begin by expressing them as a product of their prime factors:
[tex]\begin{gathered} 3=3 \\ 8=2^3 \\ 12=2^2\times3 \\ \text{LCM}=2^3\times3=24 \end{gathered}[/tex]Next, we find multiples of the L.C.M in between 49 and 95.
[tex]\begin{gathered} 24\times2=48 \\ 24\times3=72 \\ 24\times4=96 \end{gathered}[/tex]The only number that she could choose is 72.
Please help me with my calc hw, I'd be more than happy to chip in albeit with my limited knowledge.
Answers
Given:
[tex]F(x)=\int_0^x\sqrt{36-t^2}dt[/tex]Required:
To find the range of the given function.
Explanation:
The graph of the function
[tex]y=\sqrt{36-t^2}[/tex]is upper semicircle with center (0,0) and radius 6, with
[tex]-6\leq t\leq6[/tex]So,
[tex]\int_0^x\sqrt{36-t^2}dt[/tex]is the area of the portion of the right half of the semicircle that lies between
t=0 and t=x.
When x=0, the value of the integral is also 0.
When x=6, the value of the integral is the area of the quarter circle, which is
[tex]\frac{36\pi}{4}=9\pi[/tex]Therefore, the range is
[tex][0,9\pi][/tex]Final Answer:
The range of the function is,
[tex][0,9\pi][/tex]Expand the following using the suitable identity.(-x + 2y - 3z)^2
Answers
Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.
Using the square of the sum of trinomial identity expressed as:
[tex](a+b+c)^2=a^2+b^2+c^2+2\text{ab+2ac+2bc}[/tex]From the given expression;
[tex]\begin{gathered} a=-x \\ b=2y \\ c=-3z \end{gathered}[/tex]Substitute the parameters into the identity to expand as shown:
[tex](-x+2y-3z)^2=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(-x)(-3z)_{}+2(2y)(-3z)[/tex]
Simplify the result to have:
[tex](-x+2y-3z)^2=x^2+4y^2+9z^2-4xy+6xz_{}-12yz[/tex]This gives the correct expansion using a suitable identity
A computer part costs $7 to produce and distribute. Express the profit p made by selling 300 of these parts as a function of the price of c dollars. (Do not include $ symbol in your answer)
Answers
Given:
Each part costs $7 to produce and distribute.
The total number of parts on selling is 300 to make the profit P.
To write the function expression in terms of sale price C and profit P:
As we know,
[tex]\text{Profit}=\text{Selling price-cost price}[/tex]So, if we produce 1 part and sell that part, then the profit is
[tex]P=C-7[/tex]For 300 parts, the profit is
[tex]\begin{gathered} P=300(C-7) \\ P=300C-2100 \end{gathered}[/tex]Hence, the function is expressed in terms of P and C is,
[tex]P=300C-2100[/tex]A 13-feet ladder is placed 5 feet away from a wall. What is the height at which the top of the ladder reaches the wall?
Answers
Draw the situation for a better understanding:
To find the height at which the top of the ladder reaches the wall use pythagorean theorem:
[tex]\begin{gathered} h=\sqrt[]{13^2-5^2} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}[/tex]The height at which the top of the ladder reaches the wall is 12 ft.
7^2 × 7^8. 7^a------------ = -------- = 7^b7^4 7^4
Answers
We have to find the values of a and b:
[tex]\frac{7^2\cdot7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex]We can use the laws of exponents to write:
[tex]\begin{gathered} 7^2\cdot7^8=7^a \\ 7^{2+8}=7^a \\ 7^{10}=7^a \\ 10=a \end{gathered}[/tex]Then, we can solve for b as:
[tex]\begin{gathered} \frac{7^a}{7^4}=7^b \\ 7^{a-4}=7^b \\ a-4=b \\ 10-4=b \\ 6=b \end{gathered}[/tex]Answer: a=10 and b=6
find the width of a newer 48-in TV whose screen has an aspect ratio of 16:9what is the width?
Answers
The width of the TV is 41.84-in
Explanations:The diagonal size of the TV, d= 48 in
The aspect ratio= 16 : 9
The aspect ratio is usually given in form of width : Height
Let the width = w
Let the height = h
The diagram looks like:
[tex]\begin{gathered} \frac{w}{h}=\text{ }\frac{16}{9} \\ h\text{ = }\frac{9w}{16} \end{gathered}[/tex]Using the Pythagoras theorem:
[tex]\begin{gathered} d^2=h^2+w^2 \\ 48^2\text{ = (}\frac{9w}{16})^2+w^2 \\ 2304\text{ = }\frac{81w^2}{256}+w^2 \\ \text{Multiply through by 256} \\ 589824=81w^2+256w^2 \\ 589824\text{ = }337w^2 \\ w^2\text{ = }\frac{589824}{337} \\ w^2\text{ = 1750.22} \\ w\text{ = }\sqrt[]{1750.22} \\ w\text{ = 41.84 } \end{gathered}[/tex]The width of the TV is 41.84-in
how to write the rule for the rotation on #11?
Answers
#11
If the point (x, y) is rotated 180 degrees around the origin clockwise or anti-clockwise, then its image will be (-x, -y)
We just change the sign of the coordinates
From the attached picture we can see
The parallelogram MNOP where
M = (1, -2)
N = (3, -2)
O = (4, -4)
P = (2, -4)
The parallelogram M'N'O'P' where
M' = (-1, 2)
N' = (-3, 2)
O' = (-4, 4)
P' = (-2, 4)
Since all the signs of the coordinates are changed, then
M'N'O'P' is the image of MNOP by rotation 180 degrees around the orign
The rule of transformation is
[tex]R\rightarrow(O,180^{\circ})[/tex]Simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed.
Answers
[tex]\frac{1 }{8*a^{9}*b^{12}}[/tex].
Step-by-step explanation:1. Write the expression.[tex](\frac{a^{-3} }{2b^{4} } )^{3}[/tex]
2. Solve the parenthesis by multiplying the exponents with each part of the fraction.[tex]\frac{a^{(-3*3)} }{2^{(3)} b^{(4*3)} } \\ \\\frac{a^{(-9)} }{8b^{(12)} }\\ \\\frac{a^{-9} }{8b^{12} }[/tex]
3. Move a to the denominator (the negative sign of the exponent vanishes).[tex]\frac{1 }{8b^{12} *a^{9}}\\ \\\frac{1 }{8*a^{9}*b^{12}}[/tex]
4. Express your result.[tex](\frac{a^{-3} }{2b^{4} } )^{3}=\frac{1 }{8*a^{9}*b^{12}}[/tex].
Maria made 97% of her penalty kicks in soccer. Her teammates' percentages were uniformly distributed between 65% and 80%.Select all the statements that must be true?O A The mean would decrease by omitting Maria's score.B. The median would decrease by omitting Maria's score.O c The range would decrease by omitting Maria's score.D. The interquartile range would decrease by omitting Maria's score.E The standard deviation would decrease by omitting Maria's score,
Answers
Let's evaluate each statement to check wheter they are true or not.
A. "The mean would decrease by omitting Maria's score".
The mean is the sum of all the scores divided by the number of attempts. Since Maria had a higher score, if we omitted it then the sum would decrease and by extension the mean would decrease as well.
This option is true.
B. The median would decrease by omitting Maria's score.
The median is the value on the middle of the series, if we omit Maria's score, which was one of the highest then the middle of the series should move to the left, decreasing it.
This option is true.
C. The range would decrease by omitting Maria's score.
The range of a function are the values that said function can have as an output. If we omit Maria's score then the output of the function would be only the values scored by their team mates, which would go from 65 to 80, instead of 65 to 97. Therefore the range would decrease.
This option is true.
D. The interquartile range would decrease by omitting Maria's score.
The interquartile range are the values between the 25% values of the series and the 75% values of the series. Since Maria is the highest score between her teammates, she is not considered into the IQR and the value wouldn't change by removing her score.
This option is false.
E. The standard deviation would decrease by omitting Maria's score.
The standard deviation is the mean amount of variation in a series, since all her teammates are in the range of 65% to 80% and Maria is way above on the 97% score, by taking her score out we decrease the standard deviation, because there will be less variation in the serie.
This option is true.
A fisherman drops a fishing line into the sea. The end of the fishing pole is at an elevation of 5 feet. The hook that is in the water is at an elevation of -2 feet.cessmentThe number line shows their heights. Sea level is represented by 0.1. Write an absolute value expression telling how many feet the end of the fishingpole is above sea level. Evaluate the expression.2. Write an absolute value expression telling how many feet the hook is below sealevel. Evaluate the expression. 3. If the fishing line goes straight down into the water, what is the distance betweenthe end of the pole and the hook? Explain how you found this distance.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
sea level = 0 ft
end of fishing pole = 5 ft
hook = -2 ft
Step 02:
absolute value:
distance between sea level and the end of fishing pole:
| 5 - 0| = | 5 | = 5 ft
distance between hook and sea level:
|0 - (-2)| = | 0 + 2| = |2| = 2 ft
distance between hook and the end of the fishing pole:
| 5 - (-2)| = | 5 + 2| = |7| = 7 ft
To find out the distance we must consider the entire interval.
That is the full solution.
Answer:
Given a fishing line acting as number line, find the asked distances
Explanation:
given a fishing line having its one end of the fishing pole above the water. Let this distance be denoted by 'a'.
given that the hook of this fishing line is in the water hence, below the sea level. Let this depth be denoted by 'b'.
let the height of pole from sea-level be denoted by , height of the hook from sea level be denoted by and the length between pole end and hook be
since, this fishing line is acting as a number line with sea level as . The depth of fishing hook is negative and the elevation of the pole end is positive .
hence we get expressions,
for given values the evaluation of the expressions is,
Step-by-step explanation:
HELP ASAP 15 POINTS Determine which integer will make the equation true.
4x + 7 = 23
S = {3, 4, 5, 6}
3
4
5
6
Answers
Answer:
S = 4
Step-by-step explanation:
23-7 = 16
16/4 = 4
4x4+7 = 23
Answer: S = 4
Step-by-step explanation:
23 - 7 = 16
16 / 4 = 4
4 x 4 + 7 = 23
What is the most precise name for quadrilateral ABCD with vertices A(−5,7), B(6,−3), C(10,2), and D(−1,12)?A. rectangleB. parallelogramC. squareD. rhombus
Answers
Answer:
A. Rectangle
Step-by-step explanation:
A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keyloggingprograms reported grew approximately exponentially from 0.3 thousand programs in 2001 to 11.0 thousand programs in 2008. Predict the number of keyloggingprograms that will be reported in 2013
Answers
Exponential growth (EG):
2001 = 0.3
2008 = 11
2013 = ?
[tex]n\text{ = }a\times b^t[/tex]a = initial amount = 0.3
b= growth factor = ?
t = period = 7
n = 11
[tex]\begin{gathered} 11=0.3\times b^7 \\ b^7=\frac{11}{0.3} \\ b\text{ = }\sqrt[7]{\frac{11}{0.3}} \\ b=1.67 \end{gathered}[/tex]b = 1.67
Solving the number of keylogging programs that will be reported in 2013:
[tex]\begin{gathered} n\text{ = }0.3\times1.67^{12} \\ n=144.12 \end{gathered}[/tex]A group of 38 people are going to an amusement park together. They decide to carpool to save fuel. If seven people can fit in each car, how many cars do they need to take on the outing? [?] cars 3
Answers
So, the number of people = 38
7 people can fit in a one car
so, to find the number of cars divide 38 by 7
So, the number of cars = 38/7 = 5.4
But the number of cars must be integer
so, the number of cars = 6 cars
The answer is 6 cars
a recipe call for 3/4 cup of olive oil for every 1/2 cup of vinegar. how much vinigar is needed for 2 cups of olive oil? how do I solve this step by step?
Answers
The amount of vinegar needed is 1 (1/3) cups
What is Unitary method
Unitary method is a method of finding the value of 1 unit by using the value of multiple units or by the given quantity So that we can find the value of a given unknown quantity.
Here we have
A recipe requires 3/4 cup of olive oil for every 1/2 cup of vinegar
The amount of olive oil = 2 cups
Which means 3/4 cup of olive oil requires 1/2 cup of vinegar
then the vinegar required for 1 cup of Olive oil
= (vinegar Qty ÷ olive oil Qty) × 1 cup
= (1/2) ÷ (3/4) × 1
= 1/2 / 3/4 = 2/3
Therefore,
1 cup of olive oil requires 2/3 rd cup of vinegar
Then the amount of vinegar is needed for 2 cups of olive oil
= 2 × [ the amount of vinegar required for 1 cup of olive oil ]
= 2 × (2/3) = 4/3 = 1(⅓)
The amount of vinegar needed is 1 (1/3) cups
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A person randomly selects one of four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or she must pay $ 15 to play. Determine the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks.
Answers
The person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
In the given question,
A person randomly selects one of four envelopes.
Each envelope contains a check that the person gets to keep.
However, before the person can select an envelope, he or she must pay $15 to play.
We have to determine the person's expectation if two of the envelopes contain $5 checks and two of the envelopes contain $35 checks.
As we know that when the person have to select envelope then they have to pay $15.
Total number of envelop = 4
From the 4 envelop 2 have $5 each and 2 have $35 each.
So the probability of getting envelop of $5 = 2/4 = 1/2
Probability of getting envelop of $35 = 2/4 = 1/2
Let x be the amount a person gets after selecting the envelop.
So E(x) = $5×1/2 + $35×1/2
Taking 1/2 common on both side
E(x) = 1/2 ($5+$35)
E(x) = 1/2×$40
E(x) = $20
But he have to pay $15 before selecting the envelop.
So required expectation = $20−$15 = $5
Hence, the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
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In a recent year, 26.3% of all registered doctors were female. If there were 47,400 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
Answers
From the problem statement we can write:
47,400 is 26.3% of total registered doctors
We need to convert this word equation to algebraic equation noting that,
• "is" means "="
,• "of" means "x"
Also, remember to convert the percentage to decimal by dividing by 100,
[tex]\frac{26.3}{100}=0.263[/tex]The algebraic equation, thus, is:
[tex]47,400=0.263\times\text{total}[/tex]We let total be "t" and solve :
[tex]\begin{gathered} 47,400=0.263t \\ t=\frac{47,400}{0.263} \\ t=180228.14 \end{gathered}[/tex]Rounding to the nearest whole number,
Total Registered Doctors = 180,228
Answer:
180,228find the reference angle for -0.8pi
Answers
Answer:
What is Meant by the Reference Angle? In mathematics, the reference angle is defined as the acute angle and it is measuring less than 90 degrees. It is always the smallest angle, and it makes the terminal side of an angle with the x-axis.
Please help with the question below (please try to answer in maximum 5/10 minutes).
Answers
Given
Joshira can create 1 item in 3/4 of an hour.
To find:
How many items can she create in 8 hours?
Explanation:
It is given that,
Joshira can create 1 item in 3/4 of an hour.
That implies,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }\frac{3}{4}\text{ }hour=1 \\ Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }1\text{ }hour=1\div(\frac{3}{4}) \\ =1\times\frac{4}{3} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, number of items created in 8 hours is,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }8\text{ }hours=\frac{4}{3}\times8 \\ =\frac{32}{3} \\ =\frac{30+2}{3} \\ =\frac{30}{3}+\frac{2}{3} \\ =10+\frac{2}{3} \\ =10\frac{2}{3}\text{ }items \end{gathered}[/tex]Hence, she can create 10 2/3 items in 8 hours.
5(3a-1) - 2(3a+2)=3(a+2) + vselect two expressions that are equivalent to v.
Answers
Let's solve the equation for v to identify the expressions:
[tex]\begin{gathered} 5(3a-1)-2(3a+2)=3(a+2)+v \\ 15a-5-6a-4=3a+6+v \\ 9a-9=3a+6+v \\ v=9a-3a-9-6 \\ v=6a-15 \\ v=3(2a-5) \end{gathered}[/tex]Therefore the equivalent expressions are D and E
Write the tangent ratios for LP and 4Q. If needed, reduce!P12R160Not drawn to scaletan P=tan Q =
Answers
Given: The right triangle PQR as shown
To Determine: The tangents of P and Q
Solution
Given a right triangle, the tangent of any angle can be determine
Note that the side facing the right angle is the hypothenuse, the side facing the angle is the opposite and the other side is the adjacent.
Determine the opposite and the adjacent for angle P in the triangle PQR given
[tex]\begin{gathered} Note; \\ tan\theta=\frac{opposite}{adjacent} \\ tanP=\frac{16}{12} \\ tanP=\frac{4}{3} \end{gathered}[/tex]How much would you need to deposit in an account now in order to have $5000 in the account in 15years? Assume the account earns 8% interest compounded monthly.$
Answers
A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute in the given values:
[tex]5000=P(1+\frac{0.08}{12})^{12\times15}[/tex][tex]5000=P(1.0067)^{180^{}}[/tex][tex]5000=P\times3.307[/tex][tex]P=1511.94[/tex]Hence the amount need to deposit is 1511.94 dollar.
What is the value of x in the equation −6 + x = −2? (5 points)84−4−8
Answers
Given the equation:
[tex]-6+x=-2[/tex]solving for x:
[tex]\begin{gathered} x=-2+6 \\ x=4 \end{gathered}[/tex]ANSWER
x = 4
Subtract 9 1/4 - 4 3/4 . Simplify the answer and write as a mixed number.
Answers
Upon subtracting 9 1/4 from 4 3/4 we get 18/4.
Given
9 1/4 - 4 3/4
solution:
[tex]9\frac{1}{4}[/tex] can be written as 37/4 ( 9 * 4 + 1 thus 37/4) and
[tex]4\frac{3}{4}[/tex] can be written as 19/4 ( 4 * 4 + 3 thus 19/4)
37/4 - 19/4 as 4 is the common denominator for both the fractions so take 4 as the denominator
[tex]= \frac{37-19}{4}[/tex] = 18/4 if we further simplify 18/4 = 4.5
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Find the 100-th term of the following sequence
3, 10, 17, 24, …
Also find the sum of the first 100 terms.
Answers
Answer:
696
Step-by-step explanation:
*nth term = 7n - 4
n = 100
7 × 100 - 4 = 696
So the 100th term of the following sequence is: 696
*To find the nth term:
They all increase by 7 so it is 7n3 - 7 = -4 so then it is 7n - 4Answer:
Below in bold.
Step-by-step explanation:
This is an arithmetic sequence with a1 = 3 and d = 7.
So, 100th term
= a1 + d(n - 1)
= 3 + 7(100-1)
= 696.
Sum (100) =
(n/2)[2a1 + d(n - 1)]
= 50(6 + 99*7)
= 50 * 699
= 34950.
The inequality 3x +2> x+8 is equivalent to
A. x>-12
C. x > 3
B. x > 2/2/1
D. x <3
Answers
Answer: C
Step-by-step explanation:
3x + 2 > x +8
= 3x + 2 -2 > x + 8 -2
= 3x > x + 6
= 3x - x > x - x + 6
= 2x/2 > 6/2
= x > 3
Answer:
C
Step-by-step explanation:
It is the only one that makes sense.
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