The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
In the question ,
it is given that ,
the quadratic equation is cos²x + 2 cosx - 3 = 0 ,
let cosx = a ,
So , the equation becomes , a² + 2a - 3 = 0
writing the factors using the splitting the middle term method ,
we get ,
a² [tex]+[/tex] 3a -a - 3 = 0
a(a + 3) -1(a [tex]+[/tex] 3) = 0
(a - 1)(a [tex]+[/tex] 3) = 0
which means a - 1 = 0 or a + 3 = 0
a [tex]=[/tex] 1 or a [tex]=[/tex] -3 ,
Substituting a = cosx , we get
cosx [tex]=[/tex] 1 or cosx [tex]=[/tex] -3 ,
Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .
The given question is incomplete , the complete question is
Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .
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edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a iob as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments. edith wants to earn ar reasr$185 a week working a combination of both jobs. which inequality can be used to represent the situation?
Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
Given:
Edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a job as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments.
Edith wants to earn at least $185 a week working a combination of both jobs.
Let s and l be the hours of school and library.
s + l <= 2
20s + 15l >= 185.
Therefore Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.
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Suppose you have selected a random sample of n 4 measurements from a normal distribution. Compare the standard normal z values with the corresponding t values if you were forming the following confidence intervals. (a) 80% confidence interval (b) 98% confidence interval (C) 90% confidence interval
The solutions are;
The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.
The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.
The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.
Given;
Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.
(a) 80% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.
The critical value with a level of significance is 1.28.
α = 1 - 0.80 = 0.20
α/2 = 0.10
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.
(b) 98% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.
The critical value with a level of significance is 2.33.
α = 1 - 0.98 = 0.02
α/2 = 0.01
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747
(C) 90% confidence interval:
The z-value is obtained as shown below:
The level of significance is;
Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.
The critical value with a level of significance is 1.64.
α = 1 - 0.90 = 0.10
α/2 = 0.05
The t-value is obtained as shown below;
From the information, the sample size is 4.
df = n - 1 = 4 - 1
= 3
The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.
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2.3.PS-17 Julio says, "If you subtract 14 from my number and multiply the difference by -4, the result is -48." What is Julio's number?
Answer:
12
Step-by-step explanation:
y it equal to 12 is
-48÷-4=12
A fish 12 m below the surface of the ocean swims down 3 m. Then it swims
up 9m. What is the fish's new position? Show your work.
james can go 144 miles with 12 gallons of gas in his truck.how far can he go on 17 gallons?
Answer: 204 miles
Step-by-step explanation:
differentiate 2x-3/2x+1
Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
Differentiation formula for [tex]\frac{d}{dx}(\frac{u}{v}) = \frac{v\frac{d}{dx} - v\frac{d}{dx}}{v^{2} }[/tex]
Here, u = 2x - 3
v = 2x + 1
[tex]\frac{d}{dx}u[/tex] = 2
[tex]\frac{d}{dx}v[/tex] = 2
[tex]v^{2} = (2x+1)^{2}[/tex]
[tex]= 4x^{2}+4x+1[/tex]
Putting the values,
[tex]\frac{d}{dx}(\frac{2x-3}{2x+1}) = \frac{(2x+1)(2)-(2x-3)(2)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-(4x-6)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-4x+6}{4x^{2}+4x+1}[/tex]
[tex]=\frac{8}{4x^{2}+4x+1}[/tex]
Hence, Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
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The Principal of Trinity High School wants to purchase custom tote bags for each of her teachers as a thank you gift. Each bag will be printed with the school mascot on the side. Depending on the cost, she may want to order some extra tote bags to hand out as prizes to students throughout the school year. The screen printing company says that if she orders 75 tote bags, the cost will be $635. If she orders 125 tote bags, the cost will be $1035. Assuming the cost of ordering a tote bags is a linear equation, determine the cost of ordering 110 tote bags.
From the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.
As given in the question,
Let us consider y be the cost of ordering a bag.
And x represents the number of bags to be ordered as per the cost.
It is given that Cost of ordering bags and number of tote bags represents the linear equation,
Standard form of Equation is :
y = mx + c
For order of x = 75 tote bags cost is y = $635.
635 = 75m + c __(1)
For order of x = 125 tote bags cost is y = $1035.
1035 = 125m + c ____(2)
Subtract (1) from (2) we get,
1035 = 125m + c
635 = 75m + c
400 = 50m
⇒m = 8
Substitute value of m in (1) we get,
635 = 75(8) + c
⇒c = 35
Equation is:
y = 8x + 35
When number of ordering bags x = 110 then,
y = 8(110) + 35
⇒ y = $915
Therefore, from the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.
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marko has 45 comic books in his collection and tamara has 61 comic books marko buys 4 new comic books each month and tamara buys 2 comic books each month after how many months will marko and tamara have the same number of comic books
Answer: 8 months
Step-by-step explanation:
Simplify 4√20- 3√45. Show your work.
Answer:
Answer:
- [tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
simplifying radicals
[tex]\sqrt{20}[/tex]
= [tex]\sqrt{4(5)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{5}[/tex]
and
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex]
Then
4[tex]\sqrt{20}[/tex] - 3[tex]\sqrt{45}[/tex]
= 4(2[tex]\sqrt{5}[/tex] ) - 3(3[tex]\sqrt{5}[/tex] )
= 8[tex]\sqrt{5}[/tex] - 9[tex]\sqrt{5}[/tex]
= - [tex]\sqrt{5}[/tex]
Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”
For the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.
As given in the question,
Given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by :
a. dilation followed by a rotation :
Here dilation means enlarge or reduced the original shape which is not true for the given pentagon ABCDE.
b. translation followed by a rotation :
Translation means moves around a fixed point by certain degrees that is horizontal or vertical shift.
Not true.
c. Line reflection followed by a translation:
In this case preimage is flipped across the line or get reflected.
True.
d. Line reflection followed by a line reflection:
Here fixed line is or a line is used as mirror . You get a image of the original.
Not true.
Therefore, for the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.
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3. The graph represents the cost per person at
a pottery painting
studio. Find the
rate of change.
TOTAL COST ($)
5. Find the slope of
45
988 38994
40
30
15
2-3
# OF PEOPLE
A.
12
thr
D.
Answer:
the answer is 45/100=9/50 according to my solution
6
If 12 grams of coffee costs x dollars and each
gram makes y cups of coffee, what is the cost
of one cup of coffee in terms of x and y?
A)
B)
C)
D)
12y
12x
12x
y
12y
The cost of one cup of coffee in terms of x and y is x/12y.
Given in question,
Cost of 12 grams coffee = x dollars
Cost of 1 gram coffee = x/12 dollars
1 gram coffee make cups = y
Cost of 1 cup = (x/12)/y
= x/12y
Hence, the cost of one cup of coffee in terms of x and y is x/12y.
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What is the formula of tan 45 degree Theta?
The value of tan(45°+Θ) after using trigonometric ratio is
1+tanΘ/ 1-tanΘ.
What is trigonometric ratios?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here the given,
=> tan(45°+Θ)
Now using formula ,
=> tan(a+b) = [tex]\frac{tan a+tan b}{1-tan a*tanb}[/tex]
=> tan(45°+Θ)= (tan 45°+tanΘ)/(1-tan45°*tanΘ)
We know that tan 45°=1 then ,
=> tan (45°+Θ)= 1+tanΘ/ 1-tanΘ
Hence the formula for tan (45°+Θ) is 1+tanΘ/ 1-tanΘ.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 35 pounds and each large box of paper weighs 60 pounds. There were 7 more small boxes shipped than large boxes and the total weight of all boxes was 815 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
35x + 65y = 815 and x + 7 = y are the system of equations that can be used to find the number of boxes.
What is an algebra?
One of the many different mathematical disciplines is algebra. Algebra is, broadly stated, the study of mathematical symbols and the guidelines for applying those symbols to formulas.
Given,
The weight of each small box = 35 pounds
The weight of each large box = 65pounds
The total weight of the boxes = 815pounds
There were7 times as many small boxes shipped as large boxes
Let 'x' be the number of small boxes and 'y' be the number of large boxes
The weight of 'x' small boxes = 35x pounds
The weight of 'y' large boxes = 65y pounds
The total weight of the two types of boxes together = 35x+65y
Since the total weight of the boxes is 815 pounds, we have
35x+65y = 815---------------------(1)
Since 7 more small boxes = large boxes, hence we have,
x + 7 = y ------------------------(2)
Solving both the equations we get,
x = 3.95 or 4
and, y = 10.95 or 11
The number of large boxes shipped = 11
The number of small boxes shipped = 4
∴ The number of small boxes shipped = 4 and the number of large boxes shipped = 11.
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May someone please help me!!!!!!!!!!
Answer:
below
Step-by-step explanation:
The angle dimensions given for each triangle sum to 180 °
so
(x+10) + y+15 + 70 = 180 Simplifies to
x +y = 85
and
x + 20 + 50 + 60 = 180 ° simplifies to
x = 50° use this value in the underlined equation to find y = 35°
A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in
miles, , and her running speed, in miles per hour, when she runs:
The equation that describes the proportional relationship between the distance she runs in miles, and her running speed, in miles per hour, when she runs, is:
d = 0.5v.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with intercept zero, in which the output variable is given by the multiplication of the input variable and the constant of proportionality, given as follows:
y = kx
The distance as a function of the velocity and of the time in hours, is given as follows:
d = vt.
30 minutes is half an hour, hence the constant of the proportional relationship is given as follows:
v = 0.5.
Then the equation is:
d = 0.5v.
In which:
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Use an example to explain how you can model percents greater than 100%
Point n is located at (3, 5). If point n is translated 3 units right and 2 units down, the new coordinates will be.
The revised coordinates for the indicated site are (6, 3).
Given information;
Location of Point n (3, 5). The new coordinates will be if point n is moved 2 units down and 3 units right.
To get new coordinates we have to transform given points;
Transformation of the coordinate system:
Defining new coordinate systems on the plane frequently involves coordinate transformations. The transformation's u- curves are representations of vertical lines with the form u- constant, while the v- curves are representations of horizontal lines with the form v- constant.
∴ (3, 5) ⇒ (3 + 3, 5 - 2)
⇒ (6, 3)
Hence, (6, 3) are the new coordinates of the given point.
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The table how the height and weight of a few tudent in a cla. Height (inche) Weight (pound) height weight
58 122
59 128
60 126
62 133
63 145
64 136
66 144
68 150
70 152
Complete the following entence baed on your obervation. The data eem to have a correlation coefficient cloe to _____. Thi indicate that the weight of a tudent ______ a the height of the tudent increae
Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.
What is correlation coefficient?
A statistical indicator of the strength of a linear link between two variables is the correlation coefficient. Its values may be between -1 and 1.
Main Body:
Here, value of x are =58, 59, 60, 62, 63, 64, 66, 68, 70
Value of y are, = 122, 128, 126, 133, 145, 136, 144, 150, 151.
∑x = 570, ∑y= 1236, ∑ = 36234, ∑ = 170694
∑xy=78617
Thus the correlation coefficient r =
formula is in the image,
Where n is the number of the term.
here n = 9
thus, correlation coefficient
r= [tex]\frac{9*78617- 570*1236}\sqrt{{9*36234- (570^{2} )}\sqrt{9*170794- (1235)^{2} }[/tex]
Thus, r= 0.94452987512
Which is closed to 0.95 and less than 1.
Therefore, weight of a student increases as the height of the student increases.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
x > 5 represents a line with an open circle at 5 and going indefinitely toward infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given inequality is - 3(2x - 5) < 5(2 - x).
- 6x + 15 < 10 - 5x.
- x < - 5.
x > 5 (think of moving x to make it positive).
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goes to the library to read books. When she goes to the library she always reads 3 books. She also goes to the bookstore to read books twice a week. Every time she goes to the bookstore she reads 1 book on Monday and 2 books on Thursday. Reading books is her favorite thing to do. Wendy never has a chance to read books on Saturday or Sunday. What are the possible days she goes to the library? How many books does Wendy read in 2 weeks?
The possible days Wendy goes to the library are Monday and Thursday.
The number of books that Wendy reads is 12 books.
How to calculate the value?From the information, when she goes to the library she always reads 3 books and she also goes to the bookstore to read books twice a week.
In this case, the total books read in two weeks will be:
= (2 × 3) × Number of weeks
= (2 × 3) × 2
= 6 × 2
= 12
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Write a linear equation that passes through (5,2) and (6,4). *Please*
The line of equation that passes through (5,2) and (6,4) is 4x+y=22.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given points are (5,2) and (6,4)
The equation that passes from two points (x₁,y₁) and (x₂,y₂) is,
y-y₁=m.(x-x₁)
Where m=(y₂-y₁)/(x₂-x₁)
Then linear equation,
y-y₁=(y₂-y₁)/(x₂-x₁)×(x-x₁)
Substitute the values here,
y-2=(6-2)/(4-5) ×(x-5)
y-2=4/(-1)(x-5)
y-2=20-4x
4x+y=22
So the required linear Equation is 4x+y=22.
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Kelly is knitting a scarf for her brother. It took her 13 hour to knit 38 foot of the scarf. How fast is Kelly's knitting speed, in feet per hour?
Kelly's knitting speed is 2.92 feet per hour
How to determine how fast is Kelly's knitting speedFrom the question, the given parameters are:
Length of knot = 38 foot
Time to cover this length = 13 hours
The speed of the knitting the scarf is calculated as
Speed = Length of knot /Time to cover this length
Substitute the known values in the above equation
So, we have the following equation
Speed = 38/13
Evaluating the quotient in the above equation, we have
Speed = 2.92
Hence, the speed of knotting the scarf is 2.92 feet per hour
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The rectangular floor of a classroom is 24 feet in length and 30 feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?.
The area of the floor in the scale drawing is 20 square inches.
Firstly calculating the width of scale drawing. For this we will equate the two fractions.
Length/width (rectangle) = length/width (scale drawing)
Let the width of scale drawing be x
24/30 = 4/x
x = 4×30/24
Performing multiplication on Right Hand Side of the equation
x = 120/24
Performing division on Right Hand Side of the equation
x = 5
So, the area of scale drawing = length × breadth
Area of scale drawing = 4 × 5
Performing multiplication on Right Hand Side of the equation
Area of scale drawing = 20 square inches
Hence, the area is 20 square inches.
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selecting a counter displays information about that counter's collected data as a chart type. which chart type displays the current value of each performance counter in decimal format? group of answer choices line histogram bar report stacked area
The Bar graph, Line graph and Report displays the counter in decimal format.
Selecting a counter displays information about that counter's collected data as a chart type. The bar graph, line graph and report displays the current value of each performance counter in decimal format.
Line graph: - Line graph, also known as a line chart or line plot, is commonly drawn to show how something changes over a period of time. scientists and engineers use these graphs to understand and derive meaning from large chunks of data.
Bar graph: - This are the pictorial representation of data, in the form of vertical or horizontal rectangular bars, where the length of bars are proportional to the measure of data. They are mostly used in business and finance, but they can also be found in other contexts. This can be used to show the distribution of different heights of students in a class.
Report: - A report is a document that presents information in an organized format for a specific audience and purpose. All the skills and the knowledge of the professionals are communicated through reports. Reports help the top line in decision making. A rule and balanced report also helps in problem solving.
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The original price of a scarf was $16. During a store-closing sale, a shopper saved $12 on the scarf. What percentage discount did she receive? explanation
She received a discount of 75 percent from the sale of the scarf.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the original price of the scarf is $16, the money saved during the sale is $12.
Therefore:
The Amount the scarf was bought (Discounted price) = Original Price - Money saved
Discounted price =$16 - $12 = $4
Now the discount is given as;
Discount = (Amount saved / Original price) × 100%
Discount = ($12/ $16) × 100% = 75%
Therefore the discount of 75% was received.
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The sum of two numbers is 15. One less than three times the smaller is equal to the larger. Find the numbers.
Answer:
The numbers are:
4 and 11
Step-by-step explanation:
a + b = 15 Eq. 1
3a - 1 = b Eq. 2
Replacing Eq. 2 in Eq, 1
a + (3a - 1) = 15
a + 3a = 15 + 1
4a = 16
a = 16/4
a = 4
From Eq. 1:
a + b = 15
4 + b = 15
b = 15 - 4
b = 11
Check:
From Eq. 2:
3a - 1 = b
3*4 - 1 = 11
12 - 1 = 11
HELP I WILL GIVE 30 POINTS PLUS BRAINLESIT!!
Evaluate. 34+(12+14)2⋅2 Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
Step-by-step explanation:
138
In a town, 100 people need 600 liters of water to drink everyday. At a festival time how many liters of water do they need to drink with their 50 guests?
The amount of water needed to drink with their 50 guests is 900 liters.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
In a town, 100 people need 600 liters of water to drink every day.
This can be written as,
100 people = 600 liters of water
50 guests are added.
The number of people = 100 + 50 = 150 people.
Now,
100 people = 600 liters of water
Multiply 150/100 on both sides.
150 people = 150/100 x 600 litres of water
150 people = 900 liters of water
Thus,
The amount of water needed to drink with their 50 guests is 900 liters.
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1. Which equation below is n = 2 a solution for?
3n = 6
n-1=2
9+n=12
3+n=8
The equation 3n = 6 has a solution n = 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have to find that which equation below is n = 2 a solution.
Then substitute n = 2;
3n = 6
3(2) = 6
This equation has a solution n = 2.
2. n-1=2
Then substitute n = 2;
2 - 1 = 1
The solution of the equation is not n = 2
3. 9+n=12
Then substitute n = 2;
9 + 2 = 11
The solution of the equation is not n = 2
4. 3+n=8
Then substitute n = 2;
3 + 2 = 5
The solution of the equation is not n = 2
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