Answer:
(x+4)(x-5)
Step-by-step explanation:
We can look at it by thinking of two numbers, that add up to -1 and multiply to -20. We can first do this by looking at factors of -20, which are 1, -20, -1, 20, 2, -10, -2, 10, and so on. After looking through it, we can notice that -5 and 4 added equal -1, and when multiplied equal to -20, so they work. So, we factor to (x+4)(x-5)
Answer:
(x +5) (x -4)
Step-by-step explanation:
Factors of 20:
1,20
2,10
4,5
4 and 5 combine to create 1
+5 -4 = 1
(x +5) (x -4)
1+ cos^4 x-sin^4 x = 2 cos² x
[tex]\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
the sharks are fed three times a day. During the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding, the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning. If the total weight of fish fed in a day is 1/2 of a ton, how much is fed during the feeding at night?
Fish fed during night is equal to 1/6 tons
Let the weight of the fish fed at night = X tons
In the morning, the weight of the fish fed Wm = 2/15 tons.
In the afternoon, 1/15 ton more fish fed during the morning.
∴ Weight of fish fed in afternoon Wa
= 2/15 + 1/15
= 3/15 tons
Given that,
What is the total weight?Wm + Wa + Wn = 1/2 tons
∴ 2/15 + 3/15 + Wn = 1/2
∴Wn = 1/2 - 5/15
∴ Wn = 3/6 - 2/6
∴ Wn = 1/6 tons
Fish fed during night = 1/6 tons.
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How might an architect use geometry in their work?
Answer:
Architects use geometry to study and divide space as well as draft detailed building plans. Builders and engineers rely on geometric principles to create structures safely. Designers apply geometry (along with color and scale) to make the aesthetically pleasing spaces inside. Applying geometry in design is unavoidable.
One number is 2 less than a second number. Twice the second number is 7 less than 3 times the first. Find the two numbers.
Answer : 11 and 13
Step-by-step explanation:
Let the numbers be X and Y then,
By question
X= Y - 2 .....................(i)
2Y = 3X - 7 ...............(ii)
putting the value of X from (i) on equation (ii) we get,
2Y = 3(Y - 2) - 7
2Y = 3Y - 6 - 7
2Y - 3y = - 13
-Y = - 13
Y = 13
now putting value of Y in equation (i)
X = 13 - 2= 11
hence those numbers are 11 and 13 respectively
50 POINTS!!!! PLSSS HELPPP URGENTTTT!!!! Although 300° is a special angle on the unit circle, Amanda wanted to determine its coordinates using the sum and difference formulas.
Part A: Determine cos 300° using the cosine sum identity. Be sure to include all necessary work. (5 points)
Part B: Determine sin 300° using the sine difference identity. Be sure to include all necessary work. (5 points)
Answer:
a) 1/2, b) = - sqrt(3) / 2
Step-by-step explanation:
a) Let A = 120 degree, B = 180 degree
Using cosine sum is cos(120+180) = cos(120)*cos(180) - sin(120)* sin(180)
which will give you 1/2
b) Let A = 360, B = 60 degree
Using sine difference: sin(360-60) = sin(360) cos(60) - cos(360) sin (60)
gives you -sqrt(3)/2
Cos (300°) using the cosine sum identity is 1/2.
sin (300°) using the sine difference identity is √3/2.
What are Trigonometric Ratios?Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.
The main three trigonometric ratios are sine, cosine and tangent functions.
Part A :
The cosine sum identity is,
cos (A + B) = cos (A) cos (B) - sin (A) sin (B)
We can write cos (300°) as,
cos (300°) = cos (180° + 120°)
= cos (180°) cos (120°) - sin (180°) sin (120°)
sin (180°) = 0 and cos (180°) = -1
So, cos (300°) = -cos (120°) = -(-1/2) = 1/2
Part B :
Sine difference identity is,
Sin (A - B) = sin (A) cos (B) - cos(A) sin (B)
We can write sin (300°) as,
sin (300°) = sin (360° - 60°)
= sin (360°) cos(60°) - cos(360°) sin (60°)
= - sin (60°)
= -√3 / 2
Hence the value of Cos (300°) using the cosine sum identity is 1/2 and the sin (300°) using the sine difference identity is √3/2.
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a) A market researcher investigating consumers' preference for three brands of beverages namely coffee, tea and cocoa, in Ongata town gathered the following information: From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, 185 took cocon only. Required: Present the above information in a Venn Diagram. The number of customers who took tea only. (4 marks) (2 marks) (0) (2 marks) iv) The number of customers who took coffee and tea only. The number of customers who took tea and cocoa only. The number of customers who took none of the beverages. (2 marks) 1) (2 marks)
The sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
We have:
From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, and 185 took cocoon only.
We can represent the above data by the Venn diagram as shown in the picture.
From the Venn diagram:
The number of customers who took none of the beverages
= 800 - 580 = 220
The number of customers who took tea only = 95
The number of customers who took tea and cocoa only = 70
The number of customers who took tea and coffee only = 50
The number of customers who took none of the beverages = 220
Thus, in the sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.
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The large rectangle below represents one whole.
A large rectangle with 25 equal sections, 11 of which are shaded
What percent is represented by the shaded area? is it 2.27
Answer:
See below
Step-by-step explanation:
If the whole rectangle were shaded (all 25 parts) that would be 100%
So, we can set up a proportion.
25 = 100%
11 = x
Then, cross-multiply to get,
25x = 1100
Divide both sides by 25 to solve for x
x = 44.
The x value represents the percentage shaded.
44%
4n² +7n=0 what do I do if there is no part c?
Answer:
Find the coefficients using ax^2 + bx + c = 0a = 4
b = 7
c = 0
Make the coefficient equal 1. But how do we do that? Division.4n² + 7n = 0
4/4n² + 7n/4 = 0/4
Simplify= n² + 7/4n = 0
a = 1
b = 7/4
c = 0
Complete the square using b/2².b = 7/4
(b/2)² = (7/4 ÷ 2)²
Use fraction rule.
7/4 ÷ 2² = 7/4² / 2²
square the numbers
7/4² / 2² = 49/16 ÷ 4
49/16 ÷ 4 = 49/16 × 1/4
49/16 × 1/4 = 49/64
Add to both sides of the equation using 49/64
b = 7/4
b/2 = 7/4 ÷ 2
simplify
b/2 = 7 ÷ (4 × 2)
simplify(arithmetic)
b/2 = 7/8
n² + 7/4n + 49/64 = 49/64
(n + 7/8)² = 49/64
Solve for the unknown x[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]
Next, cancel out the square on the left side.
[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]
Subtract 7/8 from both of the sides.
[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]
Simplify the left side.
[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]
That wraps it up for this equation. Hope it helped!
pls help!!! Let theta equals negative 9 times pi over 4 period
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π? (5 points)
Part B: What are the exact values of all six trigonometric functions evaluated at θ?
A coterminal angle of θ such that 0 ≤ θ ≤ 2π is equal to 7π/4 and the exact value of Sin(θ) = -1/√2.
What is a coterminal angle?A coterminal angle can be defined as an angle that share the terminal side of an angle which occupies the standard position i.e it has the same initial side.
In this scenario, all angles that are multiples of 2π and added to the given angle (-9π/4) would be coterminal. For the range [0, 2π], 8π should be added to the given angle as follows:
Coterminal angle = -9π/4 + 4π
Coterminal angle = -9π/4 + 16π/4
Coterminal angle = 7π/4.
Part B.The reference angle is given by:
7π/4 -π = 3π/4.
Therefore, the exact values of all six (6) trigonometric functions evaluated at θ are:
Sin(θ) = -1/√2.Cosec(θ) = √2.Cos(θ) = 1/√2Sec(θ) = -√2.Tan(θ) = -1.Cot(θ) = -1.Read more on coterminal angles here: https://brainly.com/question/23093580
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ZA and B are supplementary and vertical angles. What is m<B
A.180
B.135
C.45
D.90
Reason:
Vertical angles are equal to each other. Call them x. They must add to 180 degrees because they are supplementary (they are able to form a straight line).
x+x = 180
2x = 180
x = 180/2
x = 90
Ellis is going on a tour that costs $65 while on vacation. He was told to bring $118 to pay for the cost of the tour and dinner. Which of the following inequalities represents the money Ellis can spend on dinner?
A. $118 + d < $65
B. $118 + d > $65
C. $65 + d > $118
D. $65 + d < $118
Answer:
The answer should be D.
In a class test(3+) marks are given for every correct answer and (-2) marks are given for every incorrect answer (-2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores -5 marks in this test, though she has got 7 correct answers.How many questions has she attempted incorrectly?
Radhika attempted 8 questions incorrectly, while Mohini attempted 13 questions incorrectly.
The number of Radhika's incorrect attemptThe given parameters are:
Correct = +3
Wrong = -2
Let the correct attempt be x and the incorrect attempt be y.
The equation that represents the total score is:
Total = 3x - 2y
She scored a total of 20.
So, we have:
3x - 2y = 20
She got 12 correctly.
So, we have:
3 * 12 - 2y = 20
Evaluate the product
36 - 2y = 20
Subtract 36 from both sides
-2y = -16
Divide by -2
y = 8
Hence, Radhika attempted 8 questions incorrectly.
The number of Mohini's incorrect attemptIn (a), we have the equation that represents the total score is:
Total = 3x - 2y
She scored a total of -5
So, we have:
3x - 2y = -5
She got 7 correctly.
So, we have:
3 * 7 - 2y = -5
Evaluate the product
21 - 2y = -5
Subtract 21 from both sides
-2y = -26
Divide by -2
y = 13
Hence, Mohini attempted 13 questions incorrectly.
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Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)
The average value of f over the region D is 243/4
To answer the question, we need to know what the average value of a function is
What is the average value of a function?The average value of a function f(x) over an interval [a,b] is given by
[tex]\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx[/tex]
Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).
x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9
So, [tex]\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}[/tex]
So, the average value of f over the region D is 243/4
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ustrating the fine basic
1. Future Value or Present Value of a Single Sum
Compute the future value of $2,250 at a 17 percent annual rate for
30 years.
Answer:$249895.46
Step-by-step explanation:
Well, if 2250 dollars increase by 17% every year for 30 years, then it will be 2250*(1.17)^30
which would be $249895.46
so if you could increase money by 17% every year, 2250 dollars now will be worth a lot in 30 years!
A soccer league has $6,333 to buy new soccer balls. If each ball costs $3, how many balls can the league buy?
Answer: 2,111 soccer balls
Step-by-step explanation:
We will divide the total amount of money by the price per ball to find how many balls the league can buy.
$6,333 / $3 = 2,111
The league can buy 2,111 soccer balls.
Arrange the samples in order starting with the sample that gives the least variation from the expected value and ending with the sample that gives the
greatest variation.
Tiles
sample A: a sample of
10 people
sample B: a sample of
50 people
sample C: a sample of
100 people
sample D: a sample of
20 people
Sequence
C
On the basis of least variation from the expected value is:
Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C
What is Variance?
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.
Here, on the basis of least variation,
we had arranged the given sample as per their expected value.
Thus, On the basis of least variation from the expected value is:
Sample A ⇒ Sample D ⇒ Sample B ⇒ Sample C
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what is a factor of 84 but not a multiple of 3
Answer:
2
Step-by-step explanation:
3/4(2x-3) = 2/3 x+5 with detailed explanation
Answer:
x = 11
Step-by-step explanation:
3/(3(2x-3)) = 2/(3x+5)
3(2x-3) = 6x - 9
3/(6x-9) = 2/(3x+5)
3(3x+5) = 2(6x-9)
9x + 15 = 12x - 18
12x - 9x = 15 + 18
3x = 33
x = 11
Answer:
[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]
Explanation:
[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]
Distribute inside parenthesis[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]
Group the variables[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]
Add or Subtract[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]
Cross Multiply[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]
Simplify the following[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]
A group of people were asked if they had run a red light in the last year. 218 responded "yes", and 270 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.
Donovan is paying for gym classes. Each type of class has its own weekly fee. He signed up for x weeks of yoga classes and y
weeks of kickboxing classes. He paid a total of $136. The equation below describes the relationship between the number of weeks
of yoga classes and the number of weeks of kickboxing classes Donovan signed up for.
8x + 12y
-
136
The ordered pair (5,8) is a solution of the equation. What does the solution (5.8)
Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
What does the function represent?
The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:
8x + 12y = 136.
Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
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Find the missing side of this right triangle.
X
8
16
VI?]
X =
Enter the number that belongs in the green box.
Step-by-step explanation:
the missing side is given by sqrt(16² - 8²)
hence,
the number that belongs in the green box is 192
-5(x+2)=-4x-12-x+2
3x-4+2x=5(x-4)
5(x+7)=-5(x-7)
6x+2-x=-2x-2+7x
Which equation has infinitely many solutions?
Answer:
−5(x+2)=−4x−12−x+2
Step-by-step explanation:
1) −5(x+2)=−4x−12−x+2
−5x−10=−4−10−x
-5x= -5x
0=0
so, it is true for all values
Which functions are one to one ? The mapping diagram or the set of ordered pairs
The functions that are one to one are the set of ordered pairs.
What are the set of ordered pairs?It should be noted that the set of ordered pairs simply means an object that the pairs are significant.
On the other hand, a mapping diagram simply consists of two parallel columns that represents the domain and the range.
In this case, the functions that are one to one are the set of ordered pairs.
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Simplify (5x+6)(6x-4)
Answer:
I think it's 35x^2 +16x-24 listen I'm not sure yet I could be wrong
Harry buys a ream of computer paper priced at $9.99 before a 6.0%
sales tax. He uses a coupon at checkout for a 10% discount. After the
purchase he mails in a form for a $5.00 rebate. What is Harry's final
cost?
Answer:
Step-by-step explanation:
Harry buys a ream of computer paper priced at $9.99 before a 6.0%
sales tax. He uses a coupon at checkout for a 10% discount. After the
purchase he mails in a form
Determine the area, in square centimeters, of
this quarter circle with a radius of 8 cm. Use 3.14
for π and round your answer to the nearest
hundredth.
Step-by-step explanation:
quarter circle means that you just find the are and then divide it by 4.
hence,
(3.14 × 8²) ÷ 4 = answer
the answer is 50.24 cm²
hope this helps.
Answer: 6.28
Step-by-step explanation: In order to get your answer, the equation that you need to do is 8 X 3.14 / 4 to get your answer.
jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per pound ?
PLS HELP ITS DU IN 5 MIN !!!!!!!!!!!!!!!!!!!!!!
Answer:
320 cents per pound
Step-by-step explanation:
so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.
PLEASE HELP!!! 25 POINTS!!!
Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help
Answer:
O The value of f(2) is smaller than the value of f(1).
Step-by-step explanation:
First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)
The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points) a 2 should be distributed as 2y + 12; y = 6 b 2 should be distributed as 2y + 12; y = 3 c The equation should be y + 6 = 4y after division by 2; y = 2 d The equation should be y + 6 = 4y after division by 2; y = 1
Step-by-step explanation:
The wording is slightly confusing so I will just solve the equation.
2 (y + 6) = 4y
We expand the bracket
2y + 12 = 4y
We subtract 2y from both sides
12 = 2y
We divide both sides by 2
6 = y