Options for the first time:increases, remains the same, decreases Options for the second box: increases, remains the same, decreases Options for the third box: reflects over the x-axis, remains the same, reflects over the y-axis
The general form of a trigonometric function is:
[tex]A\sin (B(x-C))+D[/tex]Where B is the frequency of the function.
In our problem, A=1, C=D=0.
Then, as the value of B increases, so the frequency does. The answer to the second gap is 'increases'.
On the other hand, let P be the period and f the frequency. Those two quantities are related by the formula:
[tex]f=\frac{1}{P}[/tex]Then, if the frequency increases, the period decreases. The answer to the first gap is 'decreases'.
Finally, if B is negative we have that:
[tex]\begin{gathered} B<0,A=-B,A>0 \\ \Rightarrow\tan (Bx)=\frac{\sin(Bx)}{\cos(Bx)}=\frac{\sin(-Ax)}{\cos(-Ax)}=-\frac{\sin(Ax)}{\cos(Ax)}=-\tan (-Bx) \end{gathered}[/tex]Therefore, the function is reflected over the x-axis.
A) Write an expression for the given number trickB) Simplify the expression you came up with.
A) The expression for the given number trick = 8(x + 7)
B) 8x + 56
Explanation:
A) Pick a number:
Let the number = y
Add 7:
it becomes = y + 7
Multiply by 8:
it becomes = 8(x + 7)
The expression for the given number trick = 8(x + 7)
B) We sipmlify the expression by opening the bracket:
8(x + 7) = 8 × x + 8×7
= 8x + 56
I could really use some help understanding in answering this I keep getting the answer wrong
The general formula to calculate the simple interest is given to be:
[tex]I=P\times R\times T[/tex]where:
[tex]\begin{gathered} I=\text{ Simple Interest} \\ P=\text{ Loan Amount} \\ R=\text{ Rate in decimals} \\ T=\text{ Number of time periods (yearly)} \end{gathered}[/tex]To adjust for daily time periods, we will divide the rate by 365. Therefore, we have the following parameters:
[tex]\begin{gathered} P=300 \\ R=\frac{4}{100\times365}=\frac{1}{9152} \\ T=60 \end{gathered}[/tex]Note: We are working with the assumption that the rate is annual, although not clearly stated.
Substituting these parameters into the formula, we have:
[tex]undefined[/tex]David is planning to build a triangular garden with a border made out of wood. Two of the sides will be 16.4 feet in length. The other side will be 3.3 feet. He has a total of 37 feet. Does he have enough wood to make the border? Explain. The total length of the border is feet. This is (Type a whole number or a decimal.) the length of wood David has. He enough wood to make the border.
He had 37 feet of wood and he needs 36.1 feet of perimeter for triangular garden , as 37 > 36.2, he has enough wood to make the border.
What is perimeter?The entire distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's outline or boundary. Depending on the dimensions, the perimeter of various figures can be the same size.
Consider a triangle made of an L-length wire as an example. If all the sides are the same length, then the same wire can be used to create a square. Take a look at the illustration below, which shows the bounds of a rectangular park.
David is planning to build a triangular garden with a border made out of wood.
Two of the sides will be length = 16.4 feet
= 2 × 16.4
= 32.8 feet
The other side will be 3.3 feet
The perimeter of the triangular garden
= 32.8 + 3.3
= 36.1
Thus, He had 37 feet of wood and he needs 36.1 feet of wood, as 37 > 36.2, he has enough wood to make the border.
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The sum of two numbers is 27. Twice the smaller number plus 3 times the larger number is 70. Find the numbers.
I’m stuck on this please help :(
Answer:
The smaller number is 11 and the larger number is 16.
Step-by-step explanation:
Let x = smaller number and y = larger number. The sum of these numbers is 27, so we can make the equation x + y = 27. Twice the smaller number (2x) plus three times the larger number (3y) is 70, so we can also make the equation 2x + 3y = 70.
Now, let's take a look at that first equation, x + y = 27. Let's isolate y on one side, giving us y = -x + 27. Now, we can replace y in the second equation with that value, which will allow us to solve for x.
2x + 3y = 70
2x + 3(-x + 27) = 70
2x - 3x + 81 = 70
-x + 81 = 70
-x = -11
x = 11
So, the smaller number is 11. Again, our original equation is x + y = 27. We can now replace x with 11.
11 + y = 27
y = 16
The larger number is 16. If you have any questions or found that really confusing, let me know and I'll try to clarify for you. :)
A company wants to decrease their energy bill by 14%. If their electric bill is currently $2,900 a month, what will their bill be if they are successful? Round your answer to the nearest dollar.$______
To solve this problem, first, we will determine the 14% of $2,900 and then we will subtract that amount from $2,900.
Recall that to compute the x% of y we can use the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Using the above expression, we get that the 14% of 2,900 is:
[tex]406.[/tex]Therefore, if they succeed the next month they should receive a bill for
[tex]2900-406=2494[/tex]dollars.
Now, if they pay less than the above amount they can consider it a success.
Answer:
$2494.
Yes, that is a success.
7)Ella started exercising. Which division expression means she lost 5 pounds every 2 weeks?
According to the given data we have the following:
she lost 5 pounds every 2 weeks
Therefore, the division expression would be the following:
she lost 5 pounds every 2 weeks would be represented as the following fraction. 5/2.
Therefore, the division expression would be 5/2 that means she lost 5 pounds every 2 weeks.
A flagpole 95.2 ft. Tall is on top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 34.1° , while the angle of elevation of the bottom of the flagpole is 25.8° . Find the height of the building.
Let x be the height of the building
We will first make a sketch
[tex]\tan \theta=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan 25.8=\frac{x}{y}[/tex][tex]y=\frac{x}{\tan 25.8}[/tex][tex]\tan 34.1=\frac{95.2+x}{y}[/tex]substitute the y-value in the above
[tex]\tan 34.1=\frac{95.2+x}{\frac{x}{\tan 25.8}}[/tex][tex]\tan 34.1=(95.2+x)\text{.}\frac{tan25.8}{x}[/tex][tex]x\tan 34.1=(95.2+x)\tan 25.8[/tex]x (0.677) = (95.2 + x)0.4834
open the parenthesis
0.677x = 46.01968 + 0.4834x
subtract 0.4834x from both-side of the equation
0.677x - 0.4834x = 46.01968
0.1936x = 46.01968
Divide both-side by 0.1936
x≈ 237.7 ft
[tex]x\approx238\text{ f}eet[/tex]
Suppose 30% of Americans will take the flu shot this season. Consider a random sample of 50 people. Let X be the number of the people who will take the flu shot. What the average number of X? (Round your answer to the nearest whole number)
Using percentages we can conclude that the average number is x is 15.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, an average number of x:
A random sample is 50 people and 30% will get the flu shot.So, get 30% of 50 as follows:50/100 × 30 = 15Therefore, using percentages we can conclude that the average number is x is 15.
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cos^2x(1+tan^2x)=1 simplify
After simplifying cos^2x(1+tan^2x)=1, we get LHS = RHS.
The given equation is a trigonometric equation, that includes trigonometric ratios which basically are the ratios of sides or lengths of a right angle triangle.
To simplify the given equation, we use the identity (sec^2 x - tan^2 x = 1)
that is further (sec^2 x = 1+tan^2 x)
Lets take LHS (left hand side) first,
cos^2x(1+tan^2x)
By putting the identity in LHS equation, we get
cos^2 x (1 + tan^2 x )
cos^2 x (sec^2 x)
As we know that sec^2 = 1/cos^2
Hence, cos^2 x *(1/cos^2 x)
cos^2 is eliminated by division,
= 1 which is equal to RHS
Hence, simplified and LHS = RHS
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After simplification, the trigonometric function becomes equal to each other i.e. LHS = RHS.
What are Trigonometric Functions ?
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
What are Trigonometric Ratios used for ?In trigonometry, sin, cos and tan values are the primary functions we consider while solving trigonometric problems. These trigonometry values are used to measure the angles and sides of a right-angle triangle. Apart from sine, cosine and tangent values, the other three major values are cotangent, secant and cosecant.
To simplify the given equation, we would use the identity (sec^2x - tan^2x=1) which is (sec^2x = 1 + tan^2x)
Firstly we will solve the LHS side
cos^2x(1+tan^2x)
By inserting the identity in LHS equation, we get
cos^2x(1+tan^2x)
cos^2x(sec^2x)
As sec^2 = 1/cos^2
Therefore, cos^2x *( 1/cos^2x)
cos^2 is eliminated by division,
= 1
which is equal to RHS
Hence solved and LHS = RHS
After simplification, the trigonometric function becomes equal to each other i.e. LHS = RHS.
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How is solving a multistep inequality the same as solving a multistep equation? How is it different?
You utilize PEMDAS (parentheses, exponents, multiplication, division, add, subtract) to solve a multi-step equation, and you use the same to solve a multi-step inequality. But inequalities are tough since you have to reverse the sign when multiplying or dividing by a negative integer. And although though a multi-step equation often has 1 or 2 solutions, if you write it as x= #, you'll get the same result but with an inequality sign (or signs).
Hence the above is the difference between solving a multistep inequality and multistep equation.
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#!). Two planes leave New York at 10am, One heading for Europe at 600mph and one heading in the opposite direction at 150mph. At what time will they be 900 miles apart? How far has each traveled?
Speed = Distance / time
Distance = Speed x time
In t hours, first plane travels = 600 t miles
In t hours, the second plane travels =150 t miles
After t hours the distance between the two planes is:
(600t+150t)= 750t ( since both travel in opposite directions)
When the distance is 900 miles:
750t= 900
Solve for t:
t= 900/750
t= 1.2 hours
After 1.2 hours.
1.2 x 60 = 72 minutes = 60 +12 = 1 hour and 12 minutes
Since both leave at 10 pm:
10am + 1 hour and 12 minutes : 11:12 am
They will be 900 miles apart at 11:12 am
Each one traveled:
Plane 1:
Distance: Speed x time = 600 mph x 1.2 = 720 miles
Plane 2:
Distance = Speed x time = 150 mph x 1.2 = 180 miles
: Converting fractions to decimals using long division.
Consider a fraction
[tex]\frac{3}{7}[/tex]I'm having trouble answering this Simplifying Variable Expressions question I will have two pictures. One will be for the actual question and the other one is for the steps
Given the expression:
[tex]-7(-15w+21)+3(18-27w)[/tex]We will simplify the expression as follows:
1) using the distributive property to expand the expression:
[tex](-7)\cdot(-15w)+(-7)\cdot21+3\cdot18+3\cdot(-27w)[/tex]2) using the commutative property:
[tex]\begin{gathered} 105w-147+54-81w \\ =105w-81w-147+54 \end{gathered}[/tex]3) Combine the like terms:
[tex]=24w-93[/tex]So, the answer will be 24w - 93
Find an equation for the line with slope
m=5 and which goes through the point (8,−9).
Write your answer in the form y=mx+b
An equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
In this question, we have been given a slope of the line and a point (8, -9)
We need to find an equation of the line with slope m = 5 and which goes through the point (8, -9)
Let (x1, y1) = (8, -9)
Using the slope-point form of the line,
y - y1 = m(x - x1)
y - (-9) = 5(x - 8)
y + 9= 5x - 40
y = 5x - 40 - 9
y = 5x - 49
Therefore, an equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
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(Sin 11 pi/36)(cos pi/18) - (cos 11pi/36)(sin pi/18). I have to find the exact value
From the trigonometric identity of the sum of angles
[tex]\sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta[/tex]we ca note that
[tex]\begin{gathered} \alpha=\frac{11\pi}{36} \\ \beta=\frac{\pi}{18} \end{gathered}[/tex]Then, by substituting these values into the formula, we have
[tex]\sin (\frac{11\pi}{36}-\frac{\pi}{18})=\sin \frac{11\pi}{36}\cos \frac{\pi}{18}-\cos \frac{11\pi}{36}\sin \frac{\pi}{18}[/tex]which is the same given expression. Then, we have that
[tex]\sin (\frac{11\pi}{36}\frac{\pi}{18})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin \frac{9\pi}{36}=\sin \frac{\pi}{4}[/tex]Then, the answer is:
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]
1) how many mg are equal are in 64 hectometers?2) 52000 micrometers (um) to Gm (giga)
1) 64 * 10^5 mg 2) 5.2 * 10^-11gm
Explanation:
There is no direct conversion from mg to hectometers
The conversions available:
1 m³ = 10^-6 hm³
where hm = hectometer
Also 1 hm³ = 1 * 10 ^15 mg
64 hm³ = 64 * 1 * 10 ^15 mg
= 64 * 10 ^15 mg
1 hm³ = 1hm * 1hm * 1hm
To get 1 hm, we will find the cube root of the value in mg:
[tex]\begin{gathered} 1hm\text{ = }\sqrt[3]{10^{15}mg} \\ 1\text{ hm = }10^5mg \\ 64\text{ hm = 64}\times10^{^5}mg \end{gathered}[/tex]64 hectometers = 64 * 10^5 mg
2) 1 µm = 10^-15gm
52000 µm = 52000 * 10^-15gm
= 5.2 * 10 ^4 * 10^-15gm = 5.2 * 10^(4-15) gm
= 5.2 * 10^-11gm
x−2y=2 Find the y-intercept
Answer:
-1 trust me please
[tex] \sqrt{20} \times \sqrt{15} \times \sqrt{3} [/tex]
can you help me solve it
multi step inequalities translate the following into an algebraic inequality: 14 less than twice a number is greater than or equal to 16
Let the unknown number be x
14 less than twice a number is greater than or equal to 16
14 < 2x ≥ 16Done with the solution
John connected three resistors in series. The equivalent resistance of series resistors is the sum of the values of the individual resistors. If John used resistors which were 2.2 × 102 ohms, 3.3 × 103 ohms, and 4.7 × 104 ohms, what was the equivalent resistance? Choice 'A'5.052 × 104 ohmsChoice 'B'50.52 × 103 ohmsChoice 'C'505.2 × 105 ohmsChoice 'D'5.052 × 103 ohms
Given resistors are:
[tex]\begin{gathered} 2.2\times10^2ohms \\ 3.3\times10^3ohms \\ 4.7\times10^4ohms \end{gathered}[/tex]The equivalent resistance is the sum which is obtained below
We can re-write the values given as follow
[tex]2.2\times10^2+33\times10^2+470\times10^2[/tex]=>
[tex]505.2\times10^2\text{ohms}[/tex]We can then convert this
We will get
[tex]\begin{gathered} 505.2\times10^2\text{ohms=}5.052\times10^4ohms=50.52\times10^3ohms \\ \end{gathered}[/tex]The countries with the most widgets in the world are the United States and France. If the United States has 2006 more widgets than France and the total number of widgets is 8306. Find the number of widgets for each country.
Given:
a.) The United States has 2006 more widgets than France.
b.) The total number of widgets is 8306.
Let,
x = The number of widgets the United States has
y = The number of widgets France have
x = y + 2006 ; Since the United States has 2006 more widgets than France.
From the given scenario, we generate the following equation:
[tex]\text{ x + y = 8306}[/tex]Let's determine the value of x and y.
[tex]\text{ x + y = 8306}[/tex][tex]\text{ (}y+2006)\text{ + y =8306}[/tex][tex]\text{ }y+2006\text{ + y =8306}[/tex][tex]\text{ }y+\text{ y =8306 - }2006[/tex][tex]\text{ 2y = }6,300[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{6,300}{2}[/tex][tex]\text{ y = }3150[/tex]Therefore, France has 3150 Widgets.
Let's determine the number of fidgets the United States has. Use y = 3150 in the equation x + y = 8306.
[tex]x+y=8306[/tex][tex]x+3150=8306[/tex][tex]x=8306\text{ - }3150[/tex][tex]x=5156[/tex]Therefore, the United States has 5156 Widgets.
Just number three. 12/13-12/17 I can do the total
After doing some mathematical operations, we can conclude that Randall will earn an extra $15 a week working in an amusement park as compared to a restaurant.
What do we mean by mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).So, more money that Randall can earn in the amusement park:
Randall can work in an amusement park for $8.75 an hour, for 20 hours a week.
8.75 × 20 = $175Randall can work in a restaurant for $8.00 an hour, for 20 hours a week.
8.00 × 20 = $160Then, more money that Randall can earn in the amusement park:
$175 - $160 = $15Therefore, after doing some mathematical operations, we can conclude that Randall will earn an extra $15 a week working in an amusement park as compared to a restaurant.
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A computer program found that the line c = 2t - 89 is a good fit for the data, Use this equation to predict how many cups of lemonade Lin might sell on a day when the high temperature is 74 degrees. Enter your answer in the box below. Answer:Ocups. The high temperature this Sunday is expected to be 5 degrees warmer than the high temperature this Saturday. Using the line c = 2t - 89. how many more cups of lemonade should Lin expect to sell on Sunday than Saturday? Explain or show your reasoning. Enter your response here
Part 1. Find how many cups will Lin sell when the high temperature is 74°.
We are given the expression:
[tex]c=2t-89[/tex]Where is c is the number of cups that Lin might sell and t is the high temperature.
We have the value of the high temperature:
[tex]t=74[/tex]And to solve this problem we need to substitute t=74 into the given expression:
[tex]\begin{gathered} c=2t-89 \\ \text{Substituting t=74} \\ c=2(74)-89 \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} c=148-89 \\ c=59 \end{gathered}[/tex]Answer (for part 1): 59 cups.
Part 2. Find how many more cups of lemonade Lin should sell on Sunday than Saturday.
We will call the high temperature on Saturday "x". The number of cups that Lin Might sell for x temperature is:
[tex]c=2x-89[/tex]Now, we are told that the temperature on Sunday is expected to be 5° warmer, so we represent the high temperature on Sunday as 5 more than the temperature on Saturday (which we called x).
Thus, the temperature on Sunday is:
[tex]t=x+5[/tex]And we substitute this into the expression:
[tex]\begin{gathered} c=2t-89 \\ \text{Substituting t=x+5} \\ c=2(x+5)-89 \end{gathered}[/tex]Using the distributive property on the right-hand side of the equation:
[tex]\begin{gathered} c=2x+2\cdot5-89 \\ c=2x+10-89 \end{gathered}[/tex]Re-arranging the expression:
[tex]c=(2x-89)+10[/tex]Comparing this with the expression we got for Saturday:
[tex]\begin{gathered} \text{Saturday:} \\ c=2x-89 \\ \text{Sunday:} \\ c=(2x-89)+10 \end{gathered}[/tex]As you can see, 10 more cups were sold on Sunday than on Saturday.
Answer (for part 2): 10 more cups
Help meeee quickly, I will mark brainliest!
Answer:
adjacent and corrasopnding
Step-by-step explanation:
The table shows a proportional relationship.
x 1 2 3
y 12 24 36
Write an equation that represents the proportional relationship.
y equals 1 over 12 times x
y equals 1 over 2 times x
y = 12x
y = 2x
The equation that represents the proportional relationship of the given table of values is expressed as: y = 12x.
How to Write the Equation that Represents a Proportional Relationship?The equation, y = kx, models a proportional relationship, where:
k is represented as the constant of proportionalityx and y are the variables of the proportional relationship.First, find the constant of proportionality, k, using one point from the table, (1, 12):
Constant of Proportionality (k) = 12/1
Constant of Proportionality (k) = 12.
To write the equation of the proportional relationship, substitute k = 12 into y = kx:
y = 12x
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Simple interest earned on an investment of $1200 at 9% for 4 years
Given that P= $1200 at an interest rate r= 9% per annum and for t= 4 years, we have:
E =Prt
[tex]E=1200\cdot\:0.09\cdot\:4=432[/tex]Thus, the earnings are: E = $432.
a restaurant customer left a $1.95 as a tip. the tax was 5%, and the tip was 15% of the after-tax cost. which information is not needed to compute the bill after tax and tip? what is the total bill?
Given :
a restaurant customer left a $1.95 as a tip.
The tax = 5%
the tip was 15% of the after-tax cost
So, the information that not needed is the tax
Let the total bill = x
so, 15% of x = 1.95
[tex]\begin{gathered} 0.15\cdot x=1.95 \\ \\ x=\frac{1.95}{0.15}=13 \end{gathered}[/tex]so, the total bill = $13
17#The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.75 pounds with a standard deviation of 0.95 pounds. In a recent study, a group of 60 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.73 pounds after one week.If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 60 individuals will be 1.73 pounds or less?Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.AGAIN Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Mean (μ) = 1.75 pounds
Standard deviation (σ) = 0.95 pounds
Sample size (n) = 60
First, we define the z-score for the sample mean distribution:
[tex]Z=\frac{\bar{X}-\mu}{\sigma/\sqrt{n}}[/tex]If the mean of a sample of 60 people is 1.73 pounds, the corresponding z-score is:
[tex]Z=\frac{1.73-1.75}{0.95/\sqrt{60}}=-0.163073[/tex]Then, the probability that the mean weight loss after one week on the pill for a random sample of 60 individuals will be 1.73 pounds or less is equivalent to:
[tex]P(\bar{X}\le1.73\text{ pounds})=P(Z\le-0.163073)[/tex]Finally, using the standard normal distribution:
[tex]P(Z\leqslant-0.163073)=0.4352[/tex]What is the value of n?
Answer:
[tex]n = { \boxed{ - \frac{2}{3} }}[/tex]
Step-by-step explanation:
[tex] \frac{1}{( {\sqrt[3]{5}})^{2} } = {5}^{n} \\ [/tex]
- Change or convert the cube root into an index form; ³√x = x^⅓
[tex] \frac{1}{( {5}^{ \frac{1}{3} }) {}^{2} } = {5}^{n} \\ [/tex]
- Open the brackets by multiplying the powers; (a²)² = a²×²
[tex] \frac{1}{ {5}^{( \frac{1}{3} \times 2)} } = {5}^{n} \\ \\ \frac{1}{ {5}^{ \frac{2}{3} } } = {5}^{n} [/tex]
- Following the law of indices below;
[tex]{ \boxed{ \blue{ \pmb{( \frac{1}{ {x}^{a} } ) = {x}^{ - a} }}}}[/tex]
- Therefore;
[tex] {5}^{ - \frac{2}{3} } = {5}^{n} \\ [/tex]
- Since the bases (5) are the same, the powers are equal;
[tex]n = - \frac{2}{3} [/tex]
