The point-slope form of the equation for the line is y - 3 =1/2(x - 2)
Point-slope formFrom the question, we are to determine the point-slope form of the equation for the line
The point-slope form of the equation of a line is given by
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line
and m is the slope of the line
From the given information,
Slope, m = 1/2
and we have the point (2,3)
∴ The point-slope form of the equation for the line is
y - 3 =1/2(x - 2)
Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)
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Leticia simplified an expression. Her work is shown below.
4.5 divided by one-fourth + 2 and one-half minus 0.75 times 8
Step 1 18 + 2 and one-half minus 0.75 times 8
Step 2 18 + 1.75 times 8
Step 3 18 + 14
Step 4 32
Where did Leticia make her first mistake?
step 1
step 2
step 3
step 4
Leticia made a mistake in her step 2. She did subtraction before multiplication.
How to simplify an expression?The expression can be simplified as follows;
4.5 ÷ 0.25 + 2.5 - 0.75 × 8
Hence, using Pemdas rule,
4.5 ÷ 0.25 + 2.5 - 0.75 × 8
18 + 2.5 - 0.75 × 8
18 + 2.5 - 6 = 14.5
Therefore, she made mistake in her step 2 because she was suppose to solve the multiplication before subtraction.
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*URGENT 20 POINTS*
If the area of a regular 12-gon is 2,004 meters^2, what is the length of one of the sides? Please show how you figured this out as well.
Answer:
13.3787 m
Step-by-step explanation:
A = 3 × ( 2 + √3 ) × s2
If a is 2004 just do the reverse order and u get the answer
Condense the expression to the logarithm of a single quantity.
I'm going to be so thankful if anyone could solve this for me please... because I can't understand any of it right now.
[tex]\dfrac 12 \log_3 x - 2\log_3 (y +8)\\ \\=\log_3 x^{\tfrac 12}- \log_3(y+8)^2~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log_3 \left( \dfrac {x^{\tfrac 12}}{y+8)^2} \right)~~~~~~~~~~~~~~~~~~~~~~~~;\left[\log_b \left( \dfrac mn \right) = \log_b m - \log_b n \right][/tex]
Please help!!!!!
a bag contains four red marbles, three blue marbles, two yellow marbles, and one green marble. two marbles are drawn from the bag, one at a time, without replacement. what is the probability of drawing two blue marbles?
Answer: 1/20
Step-by-step explanation:
Given: Number of red marbles in bag = 4
Number of blue marbles in bag = 3
Number of yellow marbles in bag = 3
Total marbles = 3+3+4=10
Hope this helps!!!!
Find the difference or type
"impossible"
Answer:
hope you can understand
How do you feel about the plant
20 points!!! Which of the following functions represent the graph of? Question and answers linked below, thank you!
Answer:
the second picture shown
Step-by-step explanation:
it’s has on the x axis (-3,0) and on y axis (0,-2.26)
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L
The domain of the functionThe equation of the function is given as:
[tex]C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex]
Time can be 0 or greater but cannot be negative.
So, the domain of the function includes t ≥ 0
Set the function to 0 to determine the maximum value of t.
[tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0[/tex]
Cross multiply
[tex]-18t^2 + 54t = 0[/tex]
Factor out -18t
-18t(t - 3) = 0
Divide both sides by -18t
t - 3 = 0
Add 3 to both sides
t = 3
This means that the maximum value of t is 3
Hence, the domain of the function is 0 ≤ t ≤ 3
The greatest concentration of the medicationFrom the graph of the function (see attachment), we have the maximum value to be;
C(t) = 2
Hence, the greatest concentration of the medication is 2mg/L
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The sum of 3 numbers is 33. The second number is 2 more than the first number. The third number is 2 more than the second number. What is the smallest number?
Answer:
9
Step-by-step explanation:
The information given can be written as:
x + y + z = 33y = x + 2z = y + 2 = (x + 2) + 2 = x + 4So, x + x + 2 + x + 4 = 33. This simplified is 3x + 6 = 33
Subtract 6 from both sides: 3x = 27
Divide both sides by 3: x = 9
This means that the numbers are 9, 11, and 13, so 9 is the smallest number.
To check, we can add together 9, 11 and 13, which is 33.
Hope this helps!
If you roll a dice four times, what is the chance that you roll two 3s?
Answer:
11.57%
Step-by-step explanation:
The probability of rolling two 3s is the product of the probability of rolling two 3s and two not-3s, and the number of ways that combination of rolls can appear.
__
combinations of rollsOf the four die rolls, we want two of them to be 3s. The 3s can appear anywhere in the sequence. For example, we could have 33xx, or xx33, or any of a number of other combinations (where x is a "not 3"). The total number of ways two 3s can appear an a sequence of 4 rolls is ...
C(4, 2) = 4!/(2!(4 -2)!) = 4·3/(2·1) = 6
__
probability of two 3s and two not-3sThe probability of rolling a 3 on a fair 6-sided die with one face labeled 3 is presumed to be 1/6. Then the probability of rolling something else is ...
1 -1/6 = 5/6
So, two 3s and two not-3s in a given sequence have a probability of ...
(1/6)(1/6)(5/6)(5/6) = 25/1296
__
two 3s in 4 rollsThe probability that four rolls of the die will show exactly two 3s is the product of the probability it can happen and the number of ways it can happen:
(25/1296) × 6 = 25/216 ≈ 11.57%
_____
The attachment shows the probability function of a calculator gives the same result.
1. Kimi Skuban deposits $2,000 at the beginning of each year into an Individual Retirement Account at
Boise Bank. The account pays 7% compounded annually. How much will be in the account in 25 years?
Answer:
53500
Step-by-step explanation:
if we take 2,000 and multiply it by 0.07 the resulting percentage equates to 140, or $140, add 140 to 2,000 and multiply by 25 will yield 53500
In the diagram of right triangle GFE below, altitude FD is drawn. Which of the
following ratios is equivalent to sin E?
answers: GD/DF, GF/GE, DE/FD, FE/GE
The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The correct option is B.
What is Sine (Sinθ)?The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
In the ΔGEF, the value of Sin(E) is,
Sin(E) = GF/GE
In the ΔDEF, the value of Sin(E) is,
Sin(E) = FD/FE
Hence, the correct option is B.
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This table represents a proportional relationship between x and y.
X
2.5
3.25
2.7
3.51
2.9
3.77
3.1
4.03
What is the constant of proportionality?
Enter your answer as a decimal in the box.
The constant of proportionality of the proportional relationship between x and y is: 1.3.
How to Find the Constant of Proportionality?The constant of proportionality, k = y/x, of a proportional relationship.
To find the constant of proportionality of the relationship between x and y, select any given pair from the table, say, (2.5, 3.25).
Constant of proportionality (k) = 3.25/2.5
Constant of proportionality (k) = 1.3
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SIMPLIFY HELP !!!!!!
Simplify (-2)² + 15 ÷ 3
Answer: 9
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
e^(3x)+e^x-6=0
stuck on step u = e^x, u^3 + u - 6 = 0
The Solution to the given equation is gotten as; x = 0.4913
How to solve differential equations?We are given the equation;
e³ˣ + eˣ - 6 = 0
Let u = eˣ. Thus, our equation is now;
u³ + u - 6 = 0
Factorizing this to find the roots gives us;
u = 1.6344
Thus;
eˣ = 1.6344
x = In 1.6344
x = 0.4913
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20 cm
15 cm 8 cm
20 cm
8 cm
15 cm
Find the area of the arrow above.
[?] square centimeters
The area of the arrow given in the figure is 610 square cm
Area of composite figureThe given figure is made up of rectangle and triangle. The area is expressed as:
Area = Area of rectangle + area of triangle
Substitute the given parameters
Area of the arrow = (15*20) + 0.5(31 * 20)
Area of the arrow = 300 + 310
Area of the arrow = 610 square cm
Hence the area of the arrow given in the figure is 610 square cm
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Which equation represents h in the triangle? A) h = 6sin37° B) h = 10sin37° C) h = 6 10 sin37° D) h = 10 6 sin37°
Answer:
A
Step-by-step explanation:
Consider the left triangle within the big triangle.
Identity :
sin θ = opposite side / hypotenuse
=============================================================
Taking the sine value of the angle to find h :
⇒ sin37° = h/6
⇒ h = 6sin37°
Opposite 37 is h
Angle opposite 6 is 90
Sine rule:
h/sin37 = 6/sin90
xsin37
h = 6 x sin37/ sin90
h = 3.6108....
h = 3.6 to 1dp
A) 6xsin37= 3.6108...
B) 10xsin37 =6.018...
C) 6x 10 xsin37 = 36.108...
D) 10 x 6 x sin37 = 36.108...
Thus, answer is A
Hope this helps!
Help is this a reflection or a rotation??
My exam is on Tuesday and I’m confused
Answer:
reflection
Step-by-step explanation:
its like a mirror, if it were rotated, they wouldnt line up as the same image. think of this like looking in a mirror! :)
Find f(2) if f(x)= (x +1)^2
Answer:
9
Step-by-step explanation:
substitute the x which is x= 2, so
f(2)= (2+1)^2
=(3)^2
=9
Answer:
9
Step-by-step explanation:
can someone do this for me please?! Just the answer pls
1. Both triangles are congruent by: a. angle-angle-side congruence theorem.
Using the trigonometric ratios, we have:
2. C. 9
3. C. 4√3
4. B. sin C
What is the Angle-angle-side Congruence Theorem?The angle-angle-side congruence theorem states that two triangles are congruent to each other if they both have two pairs of corresponding congruent angles and a pair of non-included congruent side.
What is the Trigonometric Ratio?To solve any right triangle, the following Trigonometric ratios can be employed:
sin ∅ = opp/hyp
cos ∅ = adj/hyp
tan ∅ = opp/adj.
1. Both triangles can be proven to be congruent based on: a. angle-angle-side congruence theorem.
2. Given the points, A(-2, 6) and B(-2, -3), the distance between both points is:
AB = |6 - (-3)| = 9 units
The answer is: C. 9
3. Apply the sine ratio:
sin 60 = opp/hyp = m/8
m = (sin 60)(8)
m = (√3/2)(8) [sin 60 = √3/2]
m = 4√3
The answer is: C. 4√3
4. Using the sine ratio:
sin C = opp/hyp = 8/17
The answer is: B. sin C
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Martin and Linda live 855 miles apart. At the same time, they start driving toward each other on the same road. Linda’s constant rate is 35 mph. Martin’s is 60 mph. How long will it take them to meet?
Answer:
Step-by-step explanation:
Givens
Linda 35 mphMartin 60 mphdistance travelled = 855 milesFormula
Linda's speed * t + martin's speed * t = 855
s1 * t + s2 *t = 855
Solution
35*t + 60*t = 855t Combine the left
95t = 855 Divide both sides by 95
95t/95 = 855/95
t = 9
Answer
They will meet in 9 hours.
Answer:
Option (D) is correct, 9 hours.
a swimming pool is 10 feet and 14 feet long. A
concrete border was poured that was 3 feet wide
around the pool. Find the perimeter of the
concrete walk.
Answer:
72 ft
Step-by-step explanation:
The perimeter of the concrete walk is the sum of the lengths of its outside edges. Each of those is two border-widths longer than the parallel pool dimension.
__
The border width is ...
(10 ft) + 2(3 ft) = 16 ft
The border length is ...
(14 ft) + 2(3 ft) = 20 ft
The perimeter is the sum of the lengths of the four sides. It can be found using the formula ...
P = 2(L +W)
P = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft
The perimeter of the concrete walk is 72 feet.
_____
Additional comment
The term "perimeter of the concrete walk" is actually somewhat ambiguous. It could refer to the total length of all of the edges of the concrete walk. If that is the case, then the 48 foot length of the inside edge must be added to the length of the outside edge for a total of 120 feet. That is, if one were to mark the edges of the walk with tape, for example, 120 feet of tape would be needed.
Ahmed and Babar share 240g of sweets in the ration 7:3. Calculate the amount Ahmed receives
The amount received by Ahmed is 168 gm.
What is Ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
Here, let the amount received by Ahmed be 7x
and amount received by Babar be 3x
Total amount of sweets = 240 gm
Now, according to question,
7x + 3x = 240
10x = 240
x = 240/10
x = 24
Thus, the amount received by Ahmed is 7 X 24 = 168 gm and amount received by Babar = 3 X 24 = 72 gm.
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One diagonal of a rhombus has endpoints (-6, 9) and (-2, 1).
What are the endpoints of the other diagonal?
O (2, 4) and (6, 6)
O (-6, 5) and (-2, 4)
O (2, 8) and (-10, 2)
O (-10, 17) and (2,7)
(2, 8) and (-10, 2)
:)
4x what = 364
please put the calculation
Answer:
91
Step-by-step explanation:
4 x 91 = 364
To work this out, we must do the inverse operation. The inverse (opposite) of x (times or multiply) is ÷ (divide).
So, we do 364 ÷ 4 = 91
Hope this helps!
- profparis
Determine each sum or difference.
A) -3.6+(-21.9) b) -43.91-(-9.44)
Jill jogs 3/4 of a mile in 1/10 of an hour at this rate how fast does she run one mile.
10 minutes
6 minutes
8 minutes
Answer:
8 minutes
Step-by-step explanation:
Jill jogs 3/4 of a mile in 1/10 hour.
⇒ 3/4 of a mile takes 6 minutes
For one mile :
3/4 mile x 4/3 : 6 x 4/3 minutes1 mile : 2 x 4 minutes1 mile takes 8 minutes1 mile she can run
1/10÷3/44/3(1/10)4/302/15hour8/60hour8 mins
Find the volume of a sphere with a radius of 2 cm.
to the nearest hundredth.
A 10.67 cm³
B 16.75 cm³
C 33.52 cm³
D 8.37 cm³
ATTEMPTS
Answer:
C 33.52 cm³
Step-by-step explanation:
Here, we have Radius(r)=2(Given)
Volume = 4/3 πr³
= 4/3 · 22/7 · 2³
= 33.5238
Round to the nearest tenth:
C 33.52 cm³
Find the mean and median of the data. 31, 14, 18, 26, 17, 32
Answer:
The mean is 23
The median is 22
Step-by-step explanation:
To find the mean you have to do 2 steps:
Step 1: Add up all your numbers:
31 + 14 + 26 + 17 + 32 + 18
= 138
Step 2: Divide you answer by how many numbers there are(6):
138 ÷ 6
= 23
Now to find you median
First put the numbers in order:
14, 17, 18, 26, 31, 32
Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:
14, 17, 18, 26, 31, 32
Now add the 2 numbers:
18 + 26
= 44
The last step is to divide your answer by 2:
44 ÷ 2
= 22
What is the area of the sector shown in the diagram below?
14 cm
OA. 34.2 cm²
OB. 30.8 cm²
OC. 136.8 cm²
D. 4.9 cm²
The area of the sector shown in the diagram below is A = 136.8 cm²
Area of a sectorThe formula for calculating the area of a sector is expressed as:
A = r²Ф/2
Given the following
radius = 14cm
Ф = π/6
Substitute
A = (14)²π/12
A = 196(3.14)/2
A = 136.8 cm²
Hence the area of the sector shown in the diagram below is A = 136.8 cm²
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