2*k + 3 = 13
2*k = 13 - 3
2*k = 10
k = 10/2
k = 5
The verbal statement 'Three more than twice k is thirteen' translates into the mathematical equation 2k + 3 = 13. Solving this equation, we find that k equals 5. This is an example of forming and solving an algebraic equation from a word problem.
Explanation:The question asks to translate a verbal statement involving a variable into a mathematical equation. The statement is 'Three more than twice k is thirteen.' To form an equation, we first identify the mathematical operations described in the statement. 'Twice k' means we need to multiply k by 2, so we have 2k. 'Three more than' suggests an addition of 3 to the previous result, so we add 3 to 2k to get 2k + 3. Finally, 'is thirteen' tells us that this expression is equal to 13. The equation becomes 2k + 3 = 13.
To solve for k, we subtract 3 from both sides to obtain 2k = 10, and then divide by 2, resulting in k = 5. This completes the exercise of writing and solving the equation.
Example of a similar equation:
Let's say we have 'Four less than half of x is twenty.' The equation would be (1/2)x - 4 = 20. We would solve by adding 4 to get (1/2)x = 24, and then multiply by 2 to find x = 48.
what is the volume of a square pyramid with base edges 24ft and slant height 20ft
The volume of the square pyramid is: 3072 ft³
What is the volume of the square pyramid?
The volume (V) of a square pyramid can be calculated using the formula:
V = ⅓ × base area × height
The base area of a square pyramid is given by the formula:
base area = base edge²
Given that the base edges (a) is 24 ft and the slant height (s) is 20 ft, we can calculate the height (h) of the pyramid using the Pythagorean theorem.
h = √(20² - (24/2)²)
h = √256
h = 16 ft
Thus:
Volume = ⅓ * 256 * 16
Volume = 3072 ft³
Matthew earned $75 in interest on
his savings account in one year.
The bank paid a simple interest
rate of 5%. What was the initial
amount of money Matthew put
into his savings account?
Answer:
Step-by-step explanation:
The formula for simple interest is
I = Prt,
where I is the interest earned,
P is the initial investment amount,
r is the interest rate in decimal form, and
t is the time in years. For us,
I = 75,
P = ?
r = .05
t = 1
Filling in what we were given:
75 = P(.05)(1) and
.05P = 75 so
P = 1500
Evaluate: (4 + 6 ⋅
3) + 3
16
66
33
25
Answer:
25
Step-by-step explanation:
Do multiplication first 6*3 is 18 18+4 is 22 22+3 is 25
PLEASE HELP WITH THIS QUESTION
Answer:
angle bisector
Step-by-step explanation:
Definitions:
median: line that meets the middle of VX
angle bisector: line that cuts angle Y in half
altitude: line that meets VX at 90°
perpendicular bisector: line that meets VX at 90° and the middle of VX
YW does not meet VX at 90° and does not meet it in the middle. Without measurements or symbols, angle Y seems to be cut in half.
Celia uses 4 ounces of yogurt for each smoothie she makes.she makes.she has 1 quart of yogurt.how many smoothies can she make with the yogurt? explain your thinking
You can use the fact that 1 quart is equal to 32 ounces.
Next, you can use the division fact, 32 divided by 4 equals 8.
And so, Celia can make 8 smoothies.
Which of the following describes the placebo effect?
O
A. At least one block of subjects in an experiment receives only
placebos.
O
B. Subjects may respond to a treatment simply because they believe
it is affecting them.
C. Subjects receive inactive sugar pills instead of real medication.
O
D. An experiment is repeated many times with real drugs and
placebos
O
E. Subjects are prevented from knowing whether they are receiving
real drugs or placebos.
Answer:
b is the correct answer
The placebo effect describes how a person might show improvement simply because they believe a treatment is working, even if it's a dummy treatment. It's an essential aspect considered during clinical studies to distinguish between actual treatment effects and the impact of patients' expectations.
Explanation:The placebo effect is best described as the phenomenon in which a person experiences a perceived improvement in their condition or symptoms simply due to their belief in the efficacy of the treatment, even if the treatment is inactive or a 'dummy' treatment, such as a sugar pill. This is represented in the provided choices by option B. Subjects may respond to a treatment simply because they believe it is affecting them.
Notably, this effect is considered in the design of clinical trials and studies. This is typically done by using a control group that receives a placebo treatment, which allows researchers to separate the physiological effects of the treatment from psychological effects induced by expectations- a crucial aspect of medical and scientific research.
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Does (-3,5 make the equation y=X+-2 true
Answer:
No.
Step-by-step explanation:
x+(-2)=-3+(-2)=-3-2=-5, not 5.
Last year 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. Find the percent of decrease.
Answer:
17.25%.
Step-by-step explanation:
We have been given that last ear 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. We are asked to find the percent of decrease.
We will use percent decrease formula to solve our given problem as:
[tex]\text{Percent decrease}=\frac{|\text{Final - Original}|}{\text{Original}}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|211-255|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|-44|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{44}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=0.1725490\times 100\%[/tex]
[tex]\text{Percent decrease}=17.25490\%[/tex]
[tex]\text{Percent decrease}\approx 17.25\%[/tex]
Therefore, percent decrease is approximately 17.25%.
Find the value ox X:
A 20
B 18
C 15
D 11
Answer:
x =15°
Step-by-step explanation:
Given that the horizontal line is 90° to the vertical line, then both the angles have to necessarily add up to 90° i.e
(5x-10)° + 25° = 90°
5x - 10 + 25 = 90
5x + 15 = 90 (subtract 15 from both sides)
5x = 90 - 15
5x = 75 (divide both sides by 5)
x = 75 / 5 = 15°
The graphs of y=x2- 3 and y = 3x -4 intersect at
approximately
1) (0.38,-2.85), only
2) (2.62,3.85), only
3) (0.38, -2.85) and (2.62,3.85)
4) (0.38, -2.85) and (3.85,2.62)
Answer:
Option 3) (0.38, -2.85) and (2.62,3.85)
Step-by-step explanation:
we have
[tex]y=x^{2}-3[/tex] ----> equation A
[tex]y=3x-4[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs
using a graphing tool
The intersection points are (0.38,-2.85) and (2.62,3.85)
see the attached figure
therefore
The graphs intersect approximately at (0.38,-2.85) and (2.62,3.85)
50 PINTS！！！！！！！！ PLEASE HELP QUICK!!!!!!!!!!! What is the slope of the line shown in the graph? (4 points) A coordinate plane is shown with points graphed at 2 comma 2 and 0 comma 1. The points are joined by a line. −2 −1 −1 over 2 1 over 2
We are given, [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] where [tex]P_1(2,2),P_2(0,1)[/tex].
Using slope formula we obtain
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{0-2}=\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}}[/tex]
Hope this helps.
Answer:
1/2
Step-by-step explanation:
I took the test :)
(04.01 LC)
Marneshia walked of a mile in of an hour. What equation can be used to calculate her unit rate in miles per hour? (1 point)
Question 2 options:
1)
= mile per hour
2)
= miles per hour
3)
= miles per hour
4)
= mile per hou
The answer is 1 mile an hour
PLEASE HELP WILL GIVE BRAINLIEST! One fifth of the student a Riverview Elementary walk to school each day. There are 350 students in the school. How many students walk to school?
A.) 50
B.) 100
C.) 270
D.) 150
E.) 70
The right answer is Option E.
Step-by-step explanation:
Given,
Total number of students in school = 350
Students who walk to school = [tex]\frac{1}{5}\ of\ total\ students[/tex]
Number of students who walk to school = [tex]\frac{1}{5}*350[/tex]
Number of students who walk to school = 70
70 students walk to the school.
The right answer is Option E.
Keywords: fraction, division
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Final answer:
The calculation shows that 70 students at Riverview Elementary walk to school.
Explanation:
The question is asking us to calculate what fraction of the total number of students at Riverview Elementary walk to school each day.
Since one fifth of the students walk to school, we need to divide the total number of students by 5 to find the number of students who walk to school.
To find one fifth of 350 students, we calculate:
350 ÷ 5 = 70
Therefore, 70 students walk to school each day at Riverview Elementary.
In a square or rectangle. How do you find the distance from the top left corner to the bottom right corner diagonally
Answer:
You use the Pythagorean theorem.
Step-by-step explanation:
https://math.stackexchange.com/questions/33549/calculating-the-distance-from-top-left-corner-to-bottom-right-corner-on-a-rectan
Find the x- and y-intercepts of the equation -5x+y=30
Answer:
x-intercept: -6y-intercept: 30Step-by-step explanation:
You can put the equation into intercept form by dividing by 30:
-5x/30 + y/30 = 1
x/(-6) + y/30 = 1
Intercept form is ...
x/(x-intercept) +y/(y-intercept) = 1
This lets us recognize the x-intercept as -6 and the y-intercept as 30.
Mr. Martin and his son are planning a fishing trip to Alaska. The rates of two companies are shown.
Wild Fishing Inc.
Round Trip Flight $200 / Daily Rate $25
Fisherman's Service
Round Trip Flight $150 / Daily Rate $30
Part A : Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?
Part B : Which company would charge $700 for 6 days for both of them?
Part C : Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.
Answer:
Part A) Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$
Part B) Wild Fishing's Inc. would charge $700 for 6 days for both of them.
Part C) Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
w = 2(200) + 2n(25) = 400 + 50n
Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
f = 2(150) + 2n(30) = 300 + 60n
Step-by-step explanation:
Part (A) Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?
The rate offered by Wild Fishing Inc:Round Trip Flight $200 / Daily Rate $25
The rate offered by Fisherman's Service:Round Trip Flight $150 / Daily Rate $30
Analyzing Wild Fishing Inc. Offer for a three day trip
As Mr. Martin and his son are planning a fishing trip to Alaska.Expenses cost for Mr. Martin and his son if they chose Wild Fishing Inc
The formula to calculate Mr Martin expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal:
Net expense faced by Mr. Martin and his son: 275 + 275 = 550$
So, Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.
Analyzing Fisherman's Service Offer for a three day trip
As Mr. Martin and his son are planning a fishing trip to Alaska.
Expenses cost for Mr. Martin and his son if they chose Fisherman's Service
The formula to calculate Mr Martin expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal:
Net expense faced by Mr. Martin and his son: 240 + 240 = 480$
So, Fisherman's Service will cost 480$ to both Mr. Martin and his son.
Choosing the right company that offers a better 3 days deal:
As we have determined that
Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.Fisherman's Service will cost 480$ to both Mr. Martin and his son.Therefore, Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$.
Part (B) Which company would charge $700 for 6 days for both of them?
Checking Wild Fishing Inc. expenses for 6 days trip:
The formula to calculate Mr Martin expenses for 6 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal for 6 days:
Net expense faced by Mr. Martin and his son: $350 + $350 = 700$
Checking Fisherman's expenses for 6 days trip:
The formula to calculate Mr Martin expenses for 6 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal for 6 days:
Net expense faced by Mr. Martin and his son: $330 + $330 = 680$
So, Wild Fishing's Inc. would charge $700 for 6 days for both of them.
Part (C) Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.
Expression for Wild Inc.
Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
w = 2 (Round trip Cost) + 2n (Daily rate)
As Round trip costs $200 and $25 is the daily rate for Wild Fishing Inc.
So, w can be written as:
w = 2(200) + 2n(25) = 400 + 50n
Expression for Wild Inc.
Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
f = 2 (Round trip Cost) + 2n (Daily rate)
As Round trip costs $150 and $30 is the daily rate for Fisherma''s Service.
So, w can be written as:
f = 2(150) + 2n(30) = 300 + 60n
Keywords: cost, expenses, deal
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6. (08.02 MC)
Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490n. What is the percent change in volume between cylinders A and b
Answer:
The percentage change in volume between cylinder A and cylinder B is 50%
Step-by-step explanation:
The volume of a cylinder is given by the formula
V= πr^2h
For cylinder A, where r=7 and h= 5, π=22/7
V= π * 7^2 * 5
V= π * 49 * 5
V= 769.69 cubic inch
For cylinder B
V= 490π
V= 1539.3804 cubic inch
The percentage change in volume between cylinder A and cylinder B
=[ (VA- VB)/VB] *100
=( 1539.3804 - 769.69) / 1539.3804
= 0.5000 * 100
= 50%
The percentage change in the volume between cylinder A and cylinder B is 50%
What is a cylinder?
A cylinder is a three-dimensional object. It is a prism with a circular base.
volume of a cylinder = πr²h
π= 22/7
r = radius
h = height
Volume of cylinder A = π(7² x 5) = 245π
Percentage change in volume = (245 / 490) - 1 = 50%
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Find the equation of the line parallel to y = 2x + 8 and passes through (4, - 6)
Answer:
y=2x-14
Step-by-step explanation:
y=2x+8
y-y1=m(x-x1)
y-(-6)=2(x-4)
y+6=2x-8
y=2x-8-6
y=2x-14
Which values of a, b , and c correctly represent the answer in the simplest form?
Answer:
a=1 b=5 c=9
Step-by-step explanation:
Answer: answer is A
Step-by-step explanation:
d/5=4 A. d=20 B. d= 4/5 C. d=5/4
Answer:
The value of A = [tex]\dfrac{1}{16}[/tex]
The value of B = [tex]\dfrac{1}{16}[/tex]
The value of C = [tex]\dfrac{25}{16}[/tex]
The value of D = [tex]\dfrac{5}{4}[/tex]
Step-by-step explanation:
Given as :
The following relations are as
[tex]\dfrac{d}{5}[/tex] =4 A ...........1
d = 20 B ...........2
d = [tex]\dfrac{4}{5}[/tex] C ...........3
And d = [tex]\dfrac{5}{4}[/tex]
Now, From the above relations
Put the value of d in eq 1
∵ 4 A = [tex]\dfrac{d}{5}[/tex]
So, d = 5 × 4 A
Or, [tex]\dfrac{5}{4}[/tex] = 20 A
∴ A = [tex]\frac{\frac{5}{4}}{20}[/tex] = [tex]\dfrac{1}{16}[/tex]
I.e The value of A = [tex]\dfrac{1}{16}[/tex]
Again
From eq 2
∵ d = 20 B
Put the value of d
So, [tex]\dfrac{5}{4}[/tex] = 20 B
Or, B = [tex]\frac{\frac{5}{4}}{20}[/tex]
∴ B = [tex]\dfrac{1}{16}[/tex]
I.e The value of B = [tex]\dfrac{1}{16}[/tex]
Similarly
From eq 3
d = [tex]\dfrac{4}{5}[/tex] C
Put the value of d
So, [tex]\dfrac{5}{4}[/tex] = [tex]\dfrac{4}{5}[/tex] C
Or, C = [tex]\frac{5\times 5}{4\times 4}[/tex]
∴ C = [tex]\dfrac{25}{16}[/tex]
I.e The value of C = [tex]\dfrac{25}{16}[/tex]
Hence The value are
The value of A = [tex]\dfrac{1}{16}[/tex]
The value of B = [tex]\dfrac{1}{16}[/tex]
The value of C = [tex]\dfrac{25}{16}[/tex]
The value of D = [tex]\dfrac{5}{4}[/tex]
Answer
Complete the steps in order to write the inverse of f(x) = x + 5
Answer:
[tex]f^{-1}[/tex](x) = x - 5
Step-by-step explanation:
Let y = f(x) and make x the subject
y = x + 5 ( subtract 5 from both sides )
y - 5 = x
Change y back into terms of x, thus
[tex]f^{-1}[/tex](x) = x - 5
I have a 100 question study guide it is worht 20 points in total how many points is it
Answer:
2000 points
Step-by-step explanation:
Given:
Number of questions in a study guide (Q) = 100
Number of points for 1 question (n) = 20
Now, total number of points is calculated using unitary method by multiplying number of questions and number of points in one question.
Therefore, the total number of points is given as:
Total points = [tex]n\times Q[/tex]
Total points = [tex]20\times 100[/tex]
Total points = [tex]2000[/tex]
Hence, the study guide is worth 2000 points.
Answer:
10
Step-by-step explanation:
Mathematics MH helpo
The inequalities that require flipping the sign are:
-5x - 10 > 5
[tex]\frac{x}{-7} + 3 \leq 4[/tex]
Solution:
Let us the inequalities one by one
You can perform on operations on both sides of inequality, and have its truth value unchanged
But if we multiply or divide by a negative number , we must flip the sign
option 1)-5x - 10 > 5
Move -10 from L.H.S to R.H.S
-5x > 5 + 10
-5x > 15
Divide the above expression by 5
[tex]-x > 3[/tex]
Divide the above inequality by -1, so we must flip the sign
x < -3
option 2)[tex]7x - 5 \leq 16[/tex]
Move the constant term from L.H.S to R.H.S
[tex]7x \leq 16 + 5\\\\7x \leq 21\\\\[/tex]
Divide the above inequality by 7
[tex]x \leq 3[/tex]
This does not required flipping the symbol
option 3[tex]\frac{x}{5} - 6 > -11[/tex]
Move the constant term from L.H.S to R.H.S
[tex]\frac{x}{5} > -11 + 6\\\\\frac{x}{5} > -5[/tex]
Multiply both the sides by 5
[tex]x > -25[/tex]
This does not required flipping the symbol
option 4[tex]x + 12 \leq 29[/tex]
Move the constant term from L.H.S to R.H.S
[tex]x \leq 29 - 12\\\\x \leq 17[/tex]
This does not required flipping the symbol
option 5[tex]\frac{x}{-7} + 3 \leq 4[/tex]
Move the constant term from L.H.S to R.H.S
[tex]\frac{x}{-7} \leq 4-3\\\\\frac{x}{-7} \leq 1\\\\[/tex]
Multiply both the sides by -7, so we must flip the sign
[tex]x \geq -7[/tex]
Thus this requires flipping the sign
Answer: -5x - 10 > 5
Step-by-step explanation:
HELP HELP I DONT UNDERSTAND THIS
Answer:
1) angle bisector
2) w = 72°
3) t = 44°
4) t = 51°
5) FG = 16 units
Step-by-step explanation:
1) Given that, ∠VYW ≅ ∠WYV
The line which cuts any angle into equal halves is angular bisector of the angle
⇒ YW is angle bisector
2) In a triangle, sum of two interior angle is equal to exterior angle of other side.
⇒ w-41° + w-31° = w.
⇒ w = 72°
3) Sum of interior angles in a pentagon is 540°
(For a n sided it is (n-2)180° )
⇒ 149° + 139° + t+32° + 3t +t = 540°
⇒ t = 44°
4) sum of all exterior angles taken one at each vertex = 360°
⇒ 2t-50° + 46° + 2t + 34° + 2t-50° + 34° + 40° = 360°
⇒ t = 51°
5) Here, by comparing ΔHGF and ΔHIF
∠GHF = ∠IHF
∠HGF = ∠HIF
and HF is common side for both triangles
⇒ ΔHGF ≡ ΔHIF ; i.e) ΔHGF , ΔHIF are congruent triangles
⇒ FG = FI = 16 units
A swimming pool is being drained so it can be cleaned. The amount of water in the pool is changing according to the función f(t)= 80,000 - 16,000t , where t = time in hours and f(t) = amount of water in liters. What is the domain of this function in this situation? Explain how you found your answer.
Answer:
0 ≤ t ≤ 5.
Step-by-step explanation:
In the function [tex]f(t)[/tex], [tex]t[/tex] is the independent variable. The domain of [tex]f[/tex] is the set of all values of [tex]t[/tex] that this function can accept.
In this case, [tex]f(t)[/tex] is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,
[tex]t \ge 0[/tex].[tex]f(t) \ge 0[/tex].The first condition is an inequality about [tex]t[/tex], which is indeed the independent variable.
However, the second condition is about [tex]f[/tex], the dependent variable of this function. It has to be rewritten as a condition about [tex]t[/tex].
[tex]\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}[/tex].
Hence, t ≤ 5.
Combine the two inequalities to obtain the domain:
0 ≤ t ≤ 5.
Simplify: 6(3 + 5)
48
65
47
15
Answer:
48
Step-by-step explanation:
Step #1, Use PEMDAS,(Purple,Eyed,Monster,Drinks,A,Soda
Step #2, Add (3+5)
(8)
Step #3, Multiply 8×6
Step #4, No You
Answer:
48
Step-by-step explanation:
Which equation can be solved to find one of the missing side lengths in the triangle?
60
12 units
O cos(609) = 12
O cos(600) =
O COS(60°) = 6
Answer:
[tex]cos(60^o)=\frac{a}{12}[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
In the right triangle of the figure
The cosine of the angle of 60 degrees is equal to divide the adjacent side to the angle of 60 degrees (BC) by the hypotenuse (AB)
so
[tex]cos(60^o)=\frac{BC}{AB}[/tex]
we have
[tex]BC=a\ units\\AB=12\ units[/tex]
substitute the values
[tex]cos(60^o)=\frac{a}{12}[/tex]
The correct equation that represents the side length is Cos 60 = a/12
Trigonometry identityFrom the triangle given, we have the following
Adjacent = aHypotenuse = 12Using the soh cah toa identity
Cos theta = adj/hyp
Cos 60 = a/12
Hence the correct equation that represents the side length is Cos 60 = a/12
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A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce
cans of the same soda costs $2.99. Calculate the unit price (price/ounce) of each
item and determine which is the better bargain.
Answer:
The better bargain is the case of twelve 12 ounce cans.
Step-by-step explanation:
2-liter bottle of soda:
67.6 ounces cost $1.89, then
1 ounce costs
[tex]\$1.89\div 67.6\approx \$0.028[/tex]
A case of twelve 12 ounce cans:
[tex]12\times 12=144[/tex] ounces of the same soda cost $2.99, then
1 ounce costs
[tex]\$2.99\div 144\approx \$0.021[/tex]
The better bargain is the second choice, the case of twelve 12 ounce cans.
PLEASE HELP ITS URGENT!!
Given: △ABC is isosceles; 1 ≅ 3
Prove: AB || CD
Answer:
AB ║ CD. (Proved)
Step-by-step explanation:
See the attached diagram of the triangle.
It is given that Δ ACD is an isosceles triangle.
Therefore, AC = AD and ∠ ACD = ∠ ADC, ⇒ ∠ 3 = ∠ 4 .......... (1)
Again, given that ∠ 1 = ∠ 3 ........... (2)
Now, from equations (1) and (2) we can write, ∠ 1 = ∠ 4
Now, AB and CD are two straight lines and AD is the transverse line and hence, ∠ 1 and ∠ 4 are alternate angles that are equal.
Therefore, AB and CD are parallel straight lines and AB ║ CD. (Proved)
Find the range of these numbers:
15,2,3,7,8,4,3,2,16,2,4