Kayla made two errors which are as follows :-
She should have used an open circle at the end of the rayShe should have pointed the arrow to the right.How to Graph a Linear Inequality
First, graph the "equals" line, then shade in the correct area.
There are three steps:
Rearrange the equation so "y" is on the left and everything else on the right. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).
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evaluate b-(-1/8)+c where b=2 and c=-7/4
Answer: [tex]\Large\boxed{\dfrac{3}{8} }[/tex]
Step-by-step explanation:
Given information
[tex]b=2[/tex]
[tex]c=-\dfrac{7}{4}[/tex]
Given expression
[tex]b-(-\dfrac{1}{8}) +c[/tex]
Substitute values into the expression
[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7}{4} )[/tex]
Convert the fractions into the common denominator
Least Common Multiple (LCM) of 8 and 4 = 8
[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7\times2}{4\times2} )[/tex]
[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{14}{8} )[/tex]
Simplify the parenthesis
[tex]=2+\dfrac{1}{8} -\dfrac{14}{8}[/tex]
Simplify by addition
[tex]=\dfrac{16}{8} +\dfrac{1}{8} -\dfrac{14}{8}[/tex]
[tex]=\dfrac{17}{8} -\dfrac{14}{8}[/tex]
Simplify by subtraction
[tex]\Large\boxed{=\dfrac{3}{8} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the area of the kite. 9 2 3
Answer:
33 units²
Refer to the attached page
I've shown the complete calculation over there.
Answer: 33
Step-by-step explanation:
one easy way to do it is by finding the area of the 4 triangles.
because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.
3 plus 3 plus 13.5 plus 13.5
to get 33
The controller of MingWare Ceramics Inc. wishes to prepare a cost of goods sold budget for September. The controller assembled the following information for constructing the cost of goods sold budget: Direct materials: Enamel Paint Porcelain Total Total direct materials purchases budgeted for September $35,870 $7,530 $139,890 $183,290 Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 2,980 2,710 7,150 12,840 Direct labor cost: Kiln Department Decorating Department Total Total direct labor cost budgeted for September $51,550 $149,500 $201,050 Finished goods inventories: Dish Bowl Figurine Total Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850 Desired inventory, September 30 3,720 4,590 4,360 12,670 Work in process inventories: Estimated inventory, September 1 $3,540 Desired inventory, September 30 1,980 Budgeted factory overhead costs for September: Indirect factory wages $80,400 Depreciation of plant and equipment 10,550 Power and light 5,110 Indirect materials 3,390 Total 99,450 Use the preceding information to prepare a cost of goods sold budget for September. For those boxes in which you must enter subtracted or negative numbers use a minus sign. MingWare Ceramics Inc. Cost of Goods Sold Budget For the Month Ending September 30 Finished goods inventory, September 1 $Finished goods inventory, September 1 Direct labor $Direct labor Direct materials: $- Select - - Select - $- Select - - Select - $- Select - Direct labor fill in the blank 15 - Select - - Select - $- Select - Work in process inventory, September 30 fill in the blank 22 - Select - $- Select - - Select - $- Select - 4,100
The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:
Cost of Goods Sold Budget:Beginning inventory of finished goods $11,850
Cost of goods manufactured 485,310
Ending inventory of finished goods (12,670)
Cost of Goods Sold $484,490
What is the cost of goods sold budget?The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.
The cost of goods sold budget is based on the cost of goods manufactured budget.
Data and Calculations:Direct materials: Enamel Paint Porcelain Total
Total direct materials purchases
budgeted for September $35,870 $7,530 $139,890 $183,290
Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 (2,980) (2,710) (7,150) (12,840)
Materials used in production $183,250
Direct labor cost: Kiln Department Decorating Department Total
Total direct labor cost
budgeted for September $51,550 $149,500 $201,050
Finished goods inventories: Dish Bowl Figurine Total
Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850
Desired inventory, September 30 3,720 4,590 4,360 12,670
Cost of goods manufactured budget:Work in process inventories:
Estimated inventory, September 1 $3,540
Direct materials used in production $183,250
Direct labor costs $201,050
Total factory overhead costs $99,450
Desired inventory, September 30 (1,980)
Cost of goods manufactured $485,310
Budgeted factory overhead costs for September:Indirect factory wages $80,400
Depreciation of plant and equipment 10,550
Power and light 5,110
Indirect materials 3,390
Total 99,450
Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.
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Find X:
J:58
K:70
L:111
M:121
Answer:
L
Step-by-step explanation:
interior angle formula so
(number of sides - 2)*180
2*180 = 360
you can also just take an example from a square 4*90 = 360
360-121-58-70 = 111
Solve for the value of w.
(4W-8)°
(3w+6)°
Step-by-step explanation:
4W-8=3W+6
4W-3W=6+8
W=14°
lets find the value of W in this straight line
4W-8°=180°(angle on a straight line)
collect like terms
4W=180°+8°
4W=188°
divide both sides by the coefficient of W which is 4
W=47°
if i am correct pls rate it
Which shows all of the zeros of function shown on the graph
Answer: C
Step-by-step explanation:
The zeros of a graph are where the graph intersects the x-axis.
PLEASE HELP I will give 50 points! PLEASE ANSWER CORRECTLY
In a school, 10% of the students have green eyes. Find the experimental probability that in a group of 4 students, at least one of them has green eyes. The problem has been simulated by generating random numbers. The digits 0-9 were used. Let the number "9" represent the 10% of students with green eyes. A sample of 20 random numbers is shown. 7918 7910 2546 1390 6075 2386 0793 7359 3048 1230 2816 6147 5978 5621 9732 9436 3806 5971 6173 1430 Experimental Probability = [?]% =
Answer: 45%
Step-by-step explanation:
Given:
A sample of 20 random numbers.The number "9" represents the 10% of students having green eyes.Find:
The experimental probability that in a group of 4 students, at least one of them has green eyes.The number of groups which contains 9 is 9 and the total number of groups are 20.
So,
P = 9 / 20 = 0.45 = 45%
Therefore, the experimental probability is 45%
The half-life of iron-52 is approximately 8.3 hours.How much of a 13 gram sample of iron-52 would remain after 8 hours? Round to three decimal places.
6.665 grams of the 13 grams remain after 8 hours.
How much of a 13 gram sample of iron-52 would remain after 8 hours?The decay equation for the 13 grams of iron-52 is:
[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]
Where N is the amount of iron-52, and t is the time in years.
Where we used the fact that the half-life is exactly 8.3 hours.
Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:
[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]
So 6.665 grams of the 13 grams remain after 8 hours.
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which statements are true
The true statements are;
-Both graphs are logarithmic functions
-Both graphs have been shifted and flipped (B and D).
What is a graph?A graph is a plot of information on the cartesian coordinates. The function is plotted on an x - y cartesian plane. Given the nature of function, we can understand the shape of the graph as shown.
In this case, the graph shows a flipped logarithmic function. As such, the following are true about the function;
-Both graphs are logarithmic functions
-Both graphs have been shifted and flipped
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Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
4
3
6
4
Juniors Seniors Total
2
6
Male
Female
Total
If a male student is selected at random, what is the
probability the student is a freshman.
2
3
P (Freshman | Male) = [?]%
Round to the nearest whole percent.
Enter
Answer:
2/7 = 29% (nearest percent)
Step-by-step explanation:
Calculate the totals and add them to the table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student is male
Use the given table to calculate the probability that the student is male:
[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]
And the probability that the student is a freshman and male:
[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]
To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of A given B is:
[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]
Substitute the found values into the formula:
[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]
Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).
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Find the measure of c.
Answer:
100°
Step-by-step explanation:
basically, in this situation, whatever number or angle you're given, and the number diagonally across from it are supposed to add up to 180°.
(i think its called a cyclic quadrilateral, so do with that what you will.)
Fraction how do you make 0.475 a simple fraction
Answer: 19/40
Step-by-step explanation:
First Write 0.475 as 0.4751Multiply both numerator and denominator by 10 for every number after the decimal point0.475 × 10001 × 1000 = 4751000. Reducing the fraction gives The answer
A triangle with a base of 16 cm and a height of 9 cm.
Answer: 288
Step-by-step explanation:
(16x9)x2
How many three-digit positive integers have three different digits and at least one prime digit?
The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.
What are prime numbers?The definition of a prime number is a natural number larger than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime.
The only two components in prime numbers are 1 and the number itself.
Any whole number greater than one is a prime number.
It has exactly two factors—1 and the actual number.
There is just one 2-digit even prime number.
Every pair of prime numbers is always a co-prime.
The product of prime numbers can be used to represent any number.
Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960
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ASAP help me with this question.
(6
By selling a TV for Rs 6900, a shopkeeper loses 8%. Find his cost price. What must be the price so as to make a profit of 12%?
Answer:
The selling price must be ₹8400 to make a profit of 12%======================
GivenSelling price of a TV is ₹6900,With this price the loss is 8%.To find SP to make a profit of 12%SolutionFind the cost, x:
x - 8% of x = 6900x - 0.08x = 69000.92x = 6900x = 6900/0.92x = 7500Find the price to get 12% profit:
7500 + 12% = 7500*1.12 = 8400need heeeelp please
The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]
In order to factorize the given expression, take out the common terms and then simplify further.
[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.
A number can have either positive or negative factors.
A number has a finite number of factors.
A number's factor will never be more than or equal to the provided number.
Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.
Finding a number's factors involves using the division and multiplication operations.
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1. What is the chance of landing on a number divisible by 2?
6
1
2
4
3
The chance or probability of landing on a number divisible by 2 is 1/2.
The likelihood of an event occurring is defined by probability. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
According to the question,
Total number of outcomes = 6
Favorable number of outcomes = 3
Thus, the required Probability = 3/6 =1/2
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finish this whole thing and ill give you five stars thanks and brainliest
Which statement is true?
The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).
The value of 2,674 x 5,480 + 5 is 5 times the value of 2,674 + 5,480.
The value of 6,432 x (1,860 − 6) is 6 less than the value of 6,432 x 1,860.
The value of 2,876 x (9,280 + 8) is 8 more than the value of 2,876 x 9,280.
The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The basic operations performed on an equation are addition, subtraction, multiplication and division.
The value of 8,590 − 4,586 = 4004
Half the value of 2 x (8,590 − 4,586) = (1/2) of 2 x (8,590 − 4,586) = 4004
The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).
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What is the General form of the zero of a first degree polynomial? Explained answered please
Answer:
for normalian is a function of the form FX is equal to a and x n + a n - 1 x n - 1 + ax2 into X + A1 is equal to A2 is degree per normal highest power of X is
express 350 as a product of prime factors
Answer:
2^1 × 5^2 × 7^1 = 350
Step-by-step explanation:
2, 5, 7 are prime
first step is to divide the number 350 with the prime factor 2
continue dividing the number 175 by the next smallest prime factor
stop until you can't divide anymore
https://www.cuemath.com/numbers/factors-of-350/
Pls help me with this calculus question
Answer:
5
Step-by-step explanation:
Gradient (slope) of the curve can be found by deriving a curve function.
In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.
Power Rules
[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]
Thus, using the power rules, we will have:
[tex]\displaystyle{y'=3x^2-4x+5}[/tex]
Note that deriving a constant will always result in 0.
Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.
The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.
[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]
Therefore, the slope at the point where a curve crosses y-axis will be 5.
the drawing plan for a new CrossFit studio shows a rectangle that is 19.5 inches by 15 inches, as shown below. The scale in the plan is 3in.:8ft. Find the length and width of the actual studio.
Answer:
Length = 52 ft
Width = 40 ft
Step-by-step explanation:
Given information:
length = 19.5 inwidth = 15 inscale = 3 in : 8 ftScale
[tex]\implies \sf 3 \: in : 8 \: ft[/tex]
[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]
To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:
[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]
[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]
Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.
Scale is 3in:8ft
So
1in=8/3ftLength
19.5(8/3)ft52ftWidth
15(8/3)40ftA certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
Step-by-step explanation:
the probability of 1 tested insect is killed is 60% or 0.6.
the probability that it is not killed is then 1-0.6 = 0.4.
when we test 7 insects and exactly 4 survive is the event that
3 insects are killed, 4 insects survive.
the probability for one such case is
0.6×0.6×0.6 × 0.4×0.4×0.4×0.4
how many such cases do we have ?
as many as ways we can select 4 insects out of the given 7.
these are 7 over 4 combinations :
7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35
so, the probability that exactly 4 out of 7 tested insects survive is
35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935
Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?
6+3/n-8
6+n/3-8
6+3/n+8
6+n/3+8
The option A is correct because the value of the statement is 6+3/n-8.
According to the statement
we have given that the statement and we have to write the statement in the numerical form.
So, For this purpose
we know that the given statement is
"Six more than the quotient of three and a number, decreased by eight".
In this statement "Six more than" indicates the sum between the quotient and 6.
And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.
"Decreased by eight" indicates a subtraction between the quotient an 8 units".
If we unit all parts of the statements, we would have
6+3/n-8
So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.
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Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 242424 meters per second. After 444 seconds of driving, she was 707070 meters away from the safe zone.
Let yyy represent the distance (in meters) from the safe zone after xxx seconds.
Complete the equation for the relationship between the distance and number of seconds.
The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.
Find the equation for the relationship between the distance and number of seconds:A linear function containing one dependent and one independent variable.
It can be represented using the equation,
y = mx + c
where m is the slope
It is given in the question that,
Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.
After 4 seconds of driving, she was 70 meters away from the safe zone.
Let, D(t) be the distance to the safe zone (measured in meters) and t be the time (measured in seconds)
After 4 seconds of driving, she was 70 meters away from the safe zone.
⇒ This means that at t = 4 seconds, D(4) = 70 meters
Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative
⇒ m = - 24
y = mx + c
⇒ D(t) = (-24)t + c
Put t = 4,
D(4) = (-24)4 + c
70 = -96 + c ⇒ c = 166
⇒ D(t) = 166 - 24t
Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.
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DJ Larissa is making a playlist for a friend; she is trying to decide what 10 songs to play and in what order they should be played .
Step 2. If she has her choices narrowed down to 7 blues, 3 hip-hop, 5 reggae, and 7 rock songs, and she wants to play no more 4 blues songs, how many different playlist or possible? Express your answer in scientific notation rounding to the hundredths place
The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
According to the statement
we have given that the some numbers of the songs which are added by the larrisa in her playlist.
And we have to tell the ways which are formed with the help of the combination and permutations.
So, For this purpose we know that the
The first condition we have given that the
"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.
Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.
For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.
And from this way we get the all combinations which are formed.
So, For this purpose
n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,
which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.
So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
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Answer:
Step-by-step explanation:
What are the excluded values? –4 and –1 -1/2, 1, and 4 1 1 and 4
The excluded values are x = 4 and x - 1
How to determine the excluded values?The complete question is added as an attachment
The function is given as:
(2x^2 - 7x - 4)/(x^2 - 5x + 4)
Set the denominator to 0
x^2 - 5x + 4 = 0
Expand
x^2 - x - 4x + 4 = 0
Factorize the equation
x(x -1) - 4(x - 1) = 0
This gives
(x - 4)(x - 1) = 0
Solve for x
x = 4 and x - 1
Hence, the excluded values are x = 4 and x - 1
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Answer: Its D 1 and 4
Step-by-step explanation:
I took the assignment
Whole page of geometry stuff for 50 points only do 2,3 and 4 ( serious answers only or 1 star and report )
See below for the distance between the points and the lines
How to determine the distance between the lines and the points?Question 2
The line and the points are given as:
x = y
P = (4, -2)
Rewrite the equation as:
y = x
The slope of the above equation is
m = 1
The slope of a line perpendicular to it is
m = -1
A linear equation is represented as:
y = mx + b
Substitute m = -1
y = -x + b
Substitute (4, -2) in y = -x + b
-2 = -4 + b
Solve for b
b = 2
Substitute b = 2 in y = -x + b
y = -x + 2
So, we have:
x = y and y = -x + 2
Substitute x for y
x = -x + 2
Solve for x
x = 1
Substitute x = 1 in y = x
y = 1
So, we have the following points
(1, 1) and (4, -2)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(1 - 4)² + (1 + 2)²
Evaluate
d = 3√2
Hence, the distance between x = y and P = (4, -2) is 3√2 units
Question 3
The line and the points are given as:
y = 2x + 1
Q = (2, 10)
The slope of the above equation is
m = 2
The slope of a line perpendicular to it is
m = -1/2
A linear equation is represented as:
y = mx + b
Substitute m = -1/2
y = -1/2x + b
Substitute (2, 10) in y = -1/2x + b
10 = -1/2 * 2 + b
Solve for b
b = 11
Substitute b = 11 in y = -1/2x + b
y = -1/2x + 11
So, we have:
y = 2x + 1 and y = -1/2x + 11
Substitute 2x + 1 for y
2x + 1 = -1/2x + 11
Solve for x
x = 4
Substitute x = 4 in y = 2x + 1
y = 9
So, we have the following points
(4, 9) and (2, 10)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(4 - 2)² + (9 - 10)²
Evaluate
d = √5
Hence, the distance between the line and the point is √5 units
Question 4
The line and the points are given as:
y = -x + 3
R = (-5, 0)
The slope of the above equation is
m = -1
The slope of a line perpendicular to it is
m = 1
A linear equation is represented as:
y = mx + b
Substitute m = 1
y = x + b
Substitute (-5, 0) in y = x + b
0 = 5 + b
Solve for b
b = -5
Substitute b = 5 in y = x + b
y = x + 5
So, we have:
y = x + 5 and y = -x + 3
Substitute x + 5 for y
x + 5 = -x + 3
Solve for x
x = -1
Substitute x = -1 in y = x + 3
y = 2
So, we have the following points
(-1, 2) and (-5, 0)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(-1 + 5)² + (2 - 0)²
Evaluate
d = 2√5
Hence, the distance between the line and the point is 2√5 units
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Suppose you average 82 on your first 7 test. What must you score on the eighth test to raise your average to 84?
so hmmm on average on the last 7 test, you get 82, so hmmm we could say that on each of the 7 tests you got 82, so you got 82, 7 times.
now, let's say in the 8th test, you get a grade of "g", now, if we were to get an average of all 8 tests, that means the average will simply be (82*7) + "g", and we know that's 84, so
[tex]\cfrac{(\stackrel{\textit{sum of all first seven tests}}{82+82+82+82+82+82+82})~~ + ~~g}{8}~~ = ~~84\implies \cfrac{(82\cdot 7)~~ + ~~g}{8}~~ = ~~84 \\\\\\ \cfrac{574+g}{8}=84\implies 574+g=672\implies g=672-574\implies g=98[/tex]
You must score 98 on the eighth test to raise your average to 84.
Average = Sum of all scores / Number of scores
The average score is given as 82, so the sum of the first 7 test scores would be 82 multiplied by 7.
The average to 84, we need to find the sum of all 8 test scores. Let's represent the score we need on the eighth test as "x."
Average = Sum of all scores / Number of scores
Using this equation, we can write:
84 = (Sum of the first 7 test scores + x) / 8
Multiply both sides of the equation by 8:
8 * 84 = Sum of the first 7 test scores + x
672 = Sum of the first 7 test scores + x
Subtract:
672 - Sum of the first 7 test scores = x
Substitute the sum of the first 7 test scores (82 * 7) into the equation:
x = 672 - (82 * 7)
x = 672 - 574
x = 98
Therefore, you must score 98 on the eighth test to raise your average to 84.
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