To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). The correct equations are: Y + 3 = 6(x - 8) and Y + 5 = -2/5(x + 3).
Explanation:To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). Where (x1, y1) is the given point and m is the given slope.
Question 1:
Given point: (8, 3) and slope: 6
Substituting the values into the formula, we have: y - 3 = 6(x - 8)
Therefore, the correct answer is option A: Y + 3 = 6(x - 8).
Question 2:
Given point: (-3, -5) and slope: -2/5
Substituting the values into the formula, we have: y + 5 = -2/5(x + 3)
Therefore, the correct answer is option A: Y + 5 = -2/5(x + 3).
Final answer:
The point-slope form equations for the given points and slopes are y - 3 = 6(x - 8) for the first set and y + 5 = (-2/5)(x + 3) for the second set.
Explanation:
The equation of a line in point-slope form is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line.
1. With the given point (8,3) and slope m = 6, the equation in point-slope form will be y - 3 = 6(x - 8). This corresponds to option B. Y-3=6(x-8).
2. For the given point (-3,-5) and slope m = -2/5, the point-slope form of the equation is y + 5 = (-2/5)(x + 3), which matches option A. Y+5= -2/5(x+3).
please help ... .. .....
Answer:
a. P
b. C
c. C
d. C
e. P
Step-by-step explanation:
When order matters, the count is of permutations. When order doesn't matter, then you count combinations.
_____
a. Order matters: It makes a difference to the three people chosen which one gets what color ribbon. (permutations)
__
b. Order doesn't matter. Bob and Charlie and Alice are effectively the same as Alice and Bob and Charlie. (combinations)
__
c. Order doesn't matter. (combinations)
__
d. Assuming the representative positions all have the same duties, order doesn't matter. (combinations)
__
e. The order of sprinters on a relay team matters. (permutations)
Does anyone know #11
Answer:
C. both student 1 and student 2
Step-by-step explanation:
Dilation does not change any angles, so the triangles are similar and the trig functions of corresponding angles will be identical.
The slope of CB is -1/3 and the slope of BA is 3, so they multiply together to give -1. That means the segments are at right angles and the triangle is a right triangle.
Both the premise and the conclusion of each student is correct.
Hong's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound. This month, Hong made 170 pounds of the blend, for a total cost of $858.70. How many pounds of type A coffee did he use?
Answer:
98 pounds
Step-by-step explanation:
Let A be pounds of A-type coffee and B be pounds of B-type coffee.
We can set-up two equations and solve simultaneously.
"This month, Hong made 170 pounds of the blend":
[tex]A+B=170[/tex]
"Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound ... a total cost of $858.70":
[tex]5.75A+4.10B=858.70[/tex]
Now we can multiply first equation by -5.75 and then ADD UP this new equation and equation 2 to get B. We have:
[tex](-5.75)*(A+B=170)\\-5.75A-5.75B=-977.5[/tex]
Now solving for B:
[tex]-5.75A-5.75B=-977.5\\5.75A+4.10B=858.70\\-------------\\-1.65B=-118.8\\B=72[/tex]
B = 72
Now plugging in this value into B of original first equation and solving for A gives us:
[tex]A+B=170\\A+72=170\\A=170-72\\A=98[/tex]
Thus, he used 98 pounds of Coffee A.
Put this into Y=Mx+B form please
Find the missing length. Round to the nearest tenth, if necessary.
A. 441
B. 22.5
C. 64
D. 19.4
Using the Pythagorean theorem:
21^2 = √(8^2 + x^2)
441 = √( 64 + x)
441 - 64 = √x
377 = √x
x = √377
x = 19.4
The answer is D.
-3m < 15
PLEASE HELP
Answer:
m > -5
Step-by-step explanation:
Divide your inequality by the coefficient of m, which is -3. Doing that requires you reverse the comparison symbol:
(-3m)/(-3) > (15)/(-3)
m > -5
_____
The comparison symbol is reversed whenever an inequality is multiplie or divided by a negative number. You might be able to see why when you look at the relation between a couple of integers:
-2 < -1
2 > 1 . . . . . . multiply the above by -1
Multiplying by a negative number effectively reflects the comparison across the center of the number line. As we know from looking in a mirror; reflection reverses left and right, so numbers that were farther to the right (more positive) are now farther to the left (more negative).
Which fraction is NOT equivalent to
8/12
?
A)
2/3
B)
24/36
C)
4/6
D)
6/10
PLEASE HELP QUICK!
the answer is D because 6 and 10 aren't multiples of 8 and 12
To find the fraction that is not equivalent to 8/12, simplify each given fraction and check for equivalence.
Explanation:To find which fraction is not equivalent to 8/12, we need to simplify or reduce each of the given fractions. If the simplified form of a fraction is not equal to 8/12, then it is not equivalent. Let's simplify each option:
A) 2/3 - already in simplest form, not equivalent to 8/12
B) 24/36 - can be simplified to 2/3, equivalent to 8/12
C) 4/6 - can be simplified to 2/3, equivalent to 8/12
D) 6/10 - can be simplified to 3/5, not equivalent to 8/12
Therefore, option D is NOT equivalent to 8/12.
The table shows the reduction in costs (in hundreds) after a manager found ways each month to cut back in his store. Identify the best fit mathematical model with its corresponding R^2 value and tell whether it is a good model.
Month: 1. 2. 3. 4. 5
Profit Loss: 86. 82. 72. 45. 15
A: Quadratic model, 0.997
No 0.997 is too high an R^2 value.
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
C. linear model, 0.902
No, 0.902 is too high an R^2 value.
D. linear model, 0.902
Yes, 0.902 is very close to 1.
Answer:
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
Step-by-step explanation:
In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.
_____
Comment on "better models"
A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.
Is this right idk but i need work fir it
Answer:
The answer is C 5/4
Step-by-step explanation:
When lines are parallel and you know there is a scalar factor, make the ratio by putting the original over the dilation 15:12 or 15/12 this is the ratio and after you need to reduce by dividing by the greatest common factor. 15 and 12's GCF is 3 so (15/3)/(12/3) = 5/4.
which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Start at the origin. Move 6 units to the right, then move 2 units up.
Start at the origin. Move 6 units up, then move 2 units to the right
Start at the origin. Move 6 units to the left, then move 2 units up.
Start at the origin. Move 6 units up then move 2 units to the left
The first one. Start at origin. Move 6 units to the right and up 2 units
Answer:
Option 1 - Start at the origin. Move 6 units to the right, then move 2 units up.
Step-by-step explanation:
To find : Which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?
Solution :
The point (6,2) means the x-coordinate is 6 and y-coordinate is 2.
According to graphing,
As the x-coordinate is positive it moves to right side.
So, From origin there is a shift of 6 units right.
As the y-coordinate is positive it moves to upward side.
So, From origin there is a shift of 2 units up.
Therefore, 'Start at the origin. Move 6 units to the right, then move 2 units up'.
Hence, Option 1 is correct.
given a=-3 and b=4 and c=-5, evaluate a+b/c
Answer:
1/5 = 0.2
Step-by-step explanation:
First
[a + b] / c is an algebraic expression
Then
[(-3) + (4)] / 5
[1] / 5
1/5
Best regards
Answer:
-3 4/5
Step-by-step explanation:
a+b/c
Substitute the values in
-3 + 4/-5
-3 + -4/5
-3 4/5
If the expression was (a+b)/c
then (-3 +4)/-5
We would do the parentheses first
1/-5
-1/5
A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:
Answer:
Option A: P(Male or Type B) > P(Male | Type B)
Step-by-step explanation:
Total Female = 85 type A, 12 type B ⇒ 97 Female.
Total Male = 65 type A, 38 type B ⇒ 103 Male
Total type A = 65 + 85 = 150
Total type B = 12 + 38 = 50
total number of people = 97 + 103 = 200
Then the probability would be:
P(Male | Type B) = [tex]\frac{number of male in B}{total number of male}[/tex]
= [tex]\frac{38}{103}[/tex]
= 0.368
P(Male or Type B) = [tex]\frac{total number of male + (total number of people in B - total number of male in B)}{total number of male}[/tex]
= [tex]\frac{103 + (50 - 38)}{200}[/tex]
= [tex]\frac{103 + 12}{200}[/tex]
= [tex]\frac{115}{200}[/tex]
= 0.575
Hence, P(Male or Type B) > P(Male | Type B)
I'll give brainliest if you show your work. Plz answer quickly.
Nolan used the following procedure to find an estimate for the square root of 18.
Step 1: Since 4^2=16 and 5^2= 25 and 16 < 18 < 25, the square root of 18 is between 4 and 5.
4.1^2=16.81
4.2^2=17.64
4.3^2=18.49
4.4^2=19.36
Step 3: Since 18.49 rounds to 18, 4.3 is the best approximation for the square root of 18.
In which step, if any, did Nolan make an error?
A) In step 1, the square root of 18.
is between 4 and 5 because the square root of 18 equals about 20 and 4 times 5= 20.
B) In step 2, he made a calculation error when squaring.
C) In step 3, he should have determined which square is closest to 18.
D) Nolan did not make an error.
Answer:
C) In step 3, he should have determined which square is closest to 18.
Step-by-step explanation:
17.64 also rounds to 18. 17.64 differs from 18 by ...
18 -17.64 = 0.36
whereas 18.49 differs from 18 by ...
18.49 -18 = 0.49
Hence 17.64 is closer to 18 and we might expect 4.2 to be closer to √18 than is 4.3.
___
The actual root of 18 is about 4.243, so 4.2 is a better approximation.
C) In step 3, he should have determined which square is closest to 18.
What is 7(2n+3) simplified without parenthesis
14n+21
(distribute the 7 to the values in the parenthesis)
How to solve:
In(x+3) - In(x-1) = 3
Answer:
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
Step-by-step explanation:
Take the antilog and solve in the usual way.
ln(x+3) -ln(x -1) = 3
ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log
(x +3)/(x -1) = e^3 . . . . take the antilog
x +3 = e^3·(x -1)
3 +e^3 = x(e^3 -1)
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
___
Check
This answer checks OK in the original equation:
ln(4.20958) -ln(0.20958) = 3
Isosceles △ABC (AC=BC) is inscribed in the circle k(O). Prove that the tangent to the circle at point C is parallel to AB .
Explanation:
Let M be the midpoint of AB. Then CM is the perpendicular bisector of AB. As such, center O is on CM, and OC is a radius (and CM). The tangent is perpendicular to that radius (and CM), so is parallel to AB, which is also perpendicular to CM.
If you need to go any further, you can show that triangles CMA and CMB are congruent, so (linear) angles CMA and CMB are congruent, hence both 90°.
Explain how to estimate the lateral area of a right cone with radius 5 cm and slant height 6 cm. Is your estimate an underestimate or overestimate? Explain.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The lateral area of a cone is equal to
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=5\ cm[/tex]
[tex]l=6\ cm[/tex]
assume [tex]\pi =3.14[/tex]
substitute the values
[tex]LA=(3.14)(5)(6)=94.2\ cm^{2}[/tex]
This value is an underestimate, because the assumed pi value is less than the real value
assumed value [tex]\pi =3.14[/tex]
real value [tex]\pi =3.1415926536...[/tex]
A survey was done of 902 students. The mean of their results was 26 and the standard deviation was 4. How many students responded above 35?
Answer:
11 students out of 902 responded above 35
Step-by-step explanation:
Using z-score we can find what percentage of student will be above 35. Using this percentage we can calculate how many students out of 902 scored above 35.
Mean = u = 26
Standard deviation = s = 4
Target Value = x = 35
Formula for the z score is:
[tex]\frac{x-u}{s}[/tex]
Using the values in this formula, we get:
[tex]\frac{35-26}{4} =2.25[/tex]
Using the z table we can find the percentage of values that would be 2.25 standard deviations above the mean in a normal distribution. Using the z-table we get this value to be 0.0122 or 1.22%
Thus 1.22% of the values will be above 35.
1.22% of 902 is 11 (rounded to nearest whole number)
Thus 11 students out of 902 responded above 35
Answer:
the answer is 11
Step-by-step explanation:
Find x and y for the following problem.
Answer:
x = 5/4
y = 7/4
Step-by-step explanation:
The smaller triangle and the larger one are similar, so the sides are proportional.
(x+5)/5 = 10/8
x/5 + 1 = 1/4 + 1 . . . . . divide it out
x/5 = 1/4 . . . . . . . . . . .subtract 1
x = 5/4 . . . . . . . . . . . . multiply by 5
___
For y, you can do exactly the same computations, replacing every instance of 5 with a 7. Then you get ...
y = 7/4
i need help on 2, 3 and 4 plz thank u ( :
Answer:
2. x = √3
3. y = 3√2
4. a = (2/3)√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.
___
2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x
___
3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve
12 = 2√2y
12/(2√2) = y = 6/√2 = 3√2
___
4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve
a = 2√2/3 = (2/3)√2
_____
Comment on "rationalizing the denominator"
"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:
1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n
That is, ...
1/√2 = (√2)/2 . . . . for example.
Remove the parentheses from the following expression: (+6) – (+2)
A. –6 – 2
B. 6 – 2
C. –6 + 3
D. 6 + 2
The correct answer:
B. 6 - 2
Answer:
B. 6-2
Step-by-step explanation:
We have been given expression : [tex]\left(+6\right)-\left(+2\right)[/tex]
Now we need to rewrite that expression [tex]\left(+6\right)-\left(+2\right)[/tex], without parenthesis then select which of the given choices are correct.
[tex]\left(+6\right)-\left(+2\right)[/tex]
We know that product of opposite sign is always negative sign.
Then product of - and +2 gives -2
So we can rewrite the problem as:
[tex]=6-2[/tex]
Hence choice B. 6-2 is the final answer.
assuming that the pentagon is regular, what is the area of the shaded region below? PLEASE HELP ASAP
Answer:
46.20 square units
Step-by-step explanation:
The area of a regular polygon can be found from the side length and apothem as ...
A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)
The total area of the pentagon is then ...
A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units
__
The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...
A = s^2 = 8^2 = 64 . . . . . . square units
__
Then the shaded area is ...
A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units
a triangle has a base of 15 inches and an area of 82.5 square inches. What is the height of the triangle
Area of a triangle = 1/2 x base x height.
Replace are and base to get:
82.5 = 1/2 x 15 x height
Multiply both sides by 2:
165 = 15 x height
Divide both sides by 15:
Height = 165 / 15
Height = 11 inches.
a sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. turning the radius-reduction screw on the top of the nozzle lets people the radius by up to 25 percent. to the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity.
Answer:
1590.4 square ft
Step-by-step explanation:
r=30 so you need to multiply that by 25% (30*.25=7.5)
30-7.5=22.5
A= pi(r)^2
A=pi*(22.5)^2
A=506.25pi
A=1590.43 or 1590.4 (to the nearest tenth)
Answer: 1590.4 square feet
Step-by-step explanation:
Given: The radius of the circular area = 30 feet
Now, 25% of the radius = [tex]0.25\times30=7.5[/tex] feet
If the we reduce the radius by 25%, then the radius of the circular area =
[tex]30-7.5=22.5\text{ feet}[/tex]
Now, the circular area of the spray is given by :-
[tex]\text{Area}=\pi r^2\\\\\Rightarrow\text{ Area}=(3.143.141592653)(22.5)^2\\\\\Rightarrow\text{ Area}=1590.43128088\approx1590.4\text{ ft}^2[/tex]
Therefore, the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity = 1590.4 square feet.
How many possible hands are in the card game euchre with a deck including 24 cards.
Cards are kings, queens, jacks, aces. 10s, and 9s
Each of these cars come in the four different types: hearts, spades, clubs, and diamonds
Answer:
42,504
Step-by-step explanation:
(24 x 23 x 22 x 21 x 20) / 5!
The reason for this is because there are 24 cards and each player would get 5
I hope this helps
There are 42,504 different possible hands in the game of Euchre when using a 24-card deck.
The student is asking about the number of possible hands in the card game Euchre when using a deck with 24 cards, which includes the kings, queens, jacks, aces, 10s, and 9s of the four suits: hearts, spades, clubs, and diamonds. In Euchre, each player is dealt a hand of five cards. To calculate the number of possible hands, we use the combination formula, which is C(n, k) = n! / (k!(n - k)!), where n is the total number of cards and k is the number of cards in a hand.
The calculation would go as follows: C(24, 5) = 24! / (5!(24 - 5)!) = 24! / (5!19!) = 42,504. So, there are 42,504 different possible hands in Euchre when using a 24-card deck.
Anyone know how to 1.8
Hope this helps , use SOHCAHTOA
Some
Old
Hag
Cracked
All
Her
Teeth
On
Apples
To remember, hope this helps !
Mikey worked 8 hours on Wednesday, 6 hours on Thursday, and 7 hours on Friday. His gross pay for all three days was $187.95
A. $8.95
B. $8.98
C. $28.13
D. 65.63
Answer:
Step-by-step explanation:
Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.
Total Work = 8+6+7 = 21 hours.
Gross Pay = 187.95 dollars.
Hourly Rate = (Gross pay)/(Total work) = (187.95)/21 = 8.95 dollars per hour.
Hence, option A is correct i.e. 8.95 dollars per hour.
One month Yoko rented 3 movies and 5 video games for a total of $40. The next month she rented 9 movies and 7 video games for a total of $74. Find the rental cost for each movie and each video game.
Answer:
movie: $3.75video game: $5.75Step-by-step explanation:
Two equations in two unknowns can be written:
3m +5v = 40
9m +7v = 74
These can be solved a variety of ways. One of them is using Cramer's rule. It tells you the solution to
ax +by = cdx +ey = fis given by ...
∆ = bd -eax = (bf -ec)/∆y = (cd -fa)/∆For the numbers above,
∆ = 5·9 -7·3 = 24m = (5·74 -7·40)/24 = 90/24 = 3.75v = (40·9 -74·3)/24 = 138/24 = 5.75The rental cost for each movie is $3.75; for each video game, it is $5.75.
___
The attached graph shows a graphing calculator solution to these equations.
What is the sum of the first 27 terms of the arithmetic sequence?
-15,-11,-7,-3,..
[tex]\bf -15~~,~~\stackrel{-15+4}{-11}~~,~~\stackrel{-11+4}{-7}~~,~~\stackrel{-7+4}{-3}~~~~,...\qquad \qquad \boxed{d=4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d=4\\ a_1=-15\\ n=27 \end{cases} \\\\\\ a_{27}=-15+(27-1)4\implies a_{27}=-15+(26)4 \\\\\\ a_{27}=-15+104 \implies a_{27}=89[/tex]
[tex]\bf \rule{34em}{0.25pt}\\\\ \textit{ sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=27\\ a_1=-15\\ a_{27}=89 \end{cases} \\\\\\ S_{27}=\cfrac{27(a_1+a_{27})}{2}\implies S_{27}=\cfrac{27(-15+89)}{2}\implies S_{27}=\cfrac{27(74)}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill S_{27}=999~\hfill[/tex]
A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?
Answer:
see the attachment for a graph
4.53 thousand square yards remain after 6 years
Step-by-step explanation:
The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...
a(t) = 10.2·0.85^(t-1)
The graph of this is attached.
After 6 years, the equation predicts
a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards
of island will remain.