Since we have two angles of 45° and a right angle, we can deduce the opposite and the adjacent side are the same.
Using the pythagoras theorem we have,
[tex]\begin{gathered} a^2+b^2=c^2 \\ x^2+x^2=\sqrt[]{5}^2\text{ Adding like terms we have} \\ 2x^2=5\text{ Isolating x, we get.} \\ x^2=\frac{5}{2}\text{ finding the root we have} \\ x=\sqrt[]{\frac{5}{2}}=\frac{\sqrt[]{5}}{\sqrt[]{2}} \end{gathered}[/tex]Then, we have to find the simplest radical form, with the rational denominator. Rationalizing we have.
[tex]\frac{\sqrt[]{5}}{\sqrt[]{2}}=\frac{\sqrt[]{5}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{\sqrt[]{5\cdot2}}{\sqrt[]{2\cdot2}}=\frac{\sqrt[]{10}}{\sqrt[]{4}}=\frac{\sqrt[]{10}}{2}[/tex]The final answer is
[tex]x=\frac{\sqrt[]{10}}{2}[/tex]I need help finding surface area in this problem below
Answer
Number of labels that the company can make from one sheet = 7
Explanation
We are told the eraser casing covers the whole eraser.
So, if we calculate the total surface area of one eraser box, we can obtain how many eraser boxes of this calculated surface area can be obtained from the given area of sheet.
Total area of the sheet
= (Number of eraser boxes that can be made from this sheet) × (Area of one eraser box)
Total area of the sheet = L × W = 15 × 21 = 315 square inches
Number of eraser boxes that can be made from this sheet = n = ?
Area of one eraser box = Total surface area of a cuboid
= 2 (LB + LH + BH)
For the eraser box,
L = 4 inches
B = 3 inches
H = 1.5 inches
Area of one eraser box = Total surface area of a cuboid
= 2 (LB + LH + BH)
= 2 [(4 × 3) + (4 × 1.5) + (3 × 1.5)]
= 2 [12 + 6 + 4.5)
= 2 (22.5)
= 45 square inches.
Total area of the sheet
= (Number of eraser boxes that can be made from this sheet) × (Area of one eraser box)
315 = n × 45
315 = 45n
We can rewrite this as
45n = 315
Divide both sides by 45
(45n/45) = (315/45)
n = 7 eraser boxes
Hope this Helps!!!
When gas prices are $2.94 per gallon, the annual supply for gas in New York State is 139 billion gallons
Answer:
Step-by-step explanation:
In a normally distributed data set, approximately 5% of the data is outside of 2 standard deviations of the mean.TrueFalse
ANSWER :
True
EXPLANATION :
Note that 95% of the distribution lies within two standard deviations.
So 100 - 95 = 5% lies outside of 2 standard deviations of the mean.
Therefore, the answer is True
Please help me solve my algebra 1 homework.“A show company is going to close one of its two stores and combine all the inventory “
You know that the polynomial that represents the inventory of Store A is:
[tex]\frac{1}{3}g^2+\frac{5}{2}[/tex]And this polynomial represents the inventory of Store B:
[tex]2g^2-\frac{3}{4}g+\frac{3}{4}[/tex]Then, you can set up the following Addition of Polynomials, which represents the combined inventory of Store A and Store B:
[tex](\frac{1}{3}g^2+\frac{5}{2})+(2g^2-\frac{3}{4}g+\frac{3}{4})[/tex]To simplify the expression, you only need to add the like terms (remember that the like terms have the same variables and the same exponents). Then, you get:
[tex]\begin{gathered} =\frac{1}{3}g^2+\frac{5}{2}+2g^2-\frac{3}{4}g+\frac{3}{4} \\ \\ =\frac{7}{3}g^2-\frac{3}{4}g+\frac{13}{4} \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{7}{3}g^2-\frac{3}{4}g+\frac{13}{4}[/tex]Find the angle of elevation of the sun if a 43- foot flagpole cast a shadow 68 feet long. Answer to nearest degree. Draw a picture, write a equation, and solve.
Use the information given in the exercise to draw the following triangle (it is not drawn to scale)
Let be β the angle of elevation of the sun.
Then, knowing that it is a Right Triangle (because it has an angle that measures 90 degrees), you can use the following Inverse Trigonometric Function to find the angle:
[tex]\beta=\tan ^{-1}(\frac{opposite}{adjacent})[/tex]In this case:
[tex]\begin{gathered} opposite=43 \\ adjacent=68 \end{gathered}[/tex]Then, substituting values and evaluating, you get:
[tex]\begin{gathered} \beta=\tan ^{-1}(\frac{43}{68}) \\ \\ \beta\approx32\degree \end{gathered}[/tex]Therefore, the answer is:
- Picture (It is not drawn to scale):
- Equation:
[tex]\beta=\tan ^{-1}(\frac{43}{68})[/tex]- Solution:
[tex]\beta\approx32\degree[/tex]Avery made a scale drawing of a restaurant. She used the scale 1 inch : 3 feet. In the drawing, a table in the restaurant is 2 inches long. What is the length of the actual table? ___ feet
The ratio original table to drawing table is
[tex]\text{ratio}=\frac{3\text{ f}eet}{1\text{ inch}}[/tex]Since the drawing table is 2 inches long, the actual table has
[tex]2inches\times\frac{3\text{ feet}}{\text{1 inche}}=6\text{ f}eet[/tex]Then, What is the length of the actual table? 6 feet
To purchase 511,900 worth of restaurant equipment for her business, Ina made a down payment of S1409 and took out a business loan for the rest. 23years of paying monthly payments of 5319.44, she finally paid off the loanxх5?(a) What was the total amount Jina ended up paying for the equipment(including the down payment and monthly payments)?s]How much interesa Jina pay on the ice?s]
Given:
The cost of restaurant equipment = $11,900
Jina made a down payment of $1400 and took out a business loan for the rest.
After 3 years of paying monthly payments of $319.44 she finally paid off the loan
A) The total amount Jina ended up paying for the equipment =
[tex]1400+3\cdot12\cdot319.44=12,899.84[/tex]B) The interest = 12,899.84 - 11900 = 999.84
So, the interest pay on the loan = $999.84
Complete the data table for the function f(x) = VX-5 - 1
Given the function:
[tex]f(x)=\sqrt[]{x-5}-1[/tex]We can complete the table if we make y = f(x) and evaluate each value of x on the function like this:
[tex]\begin{gathered} y=f(5)=\sqrt[]{5-5}-1=\sqrt[]{0}-1=-1 \\ y=-1 \end{gathered}[/tex]then, for the rest of the values we have:
[tex]\begin{gathered} f(6)=\sqrt[]{6-5}-1=\sqrt[]{1}-1=1-1=0 \\ f(9)=\sqrt[]{9-5}-1=\sqrt[]{4}-1=2-1=1 \\ f(14)=\sqrt[]{14-5}-1=\sqrt[]{9}-1=3-1=2 \end{gathered}[/tex]Lowest common denominator 5/9-24t • 3t-2/8t^2+5t-3
we have the expression
[tex]\frac{5}{9-24t^{}},\frac{3t-2}{8t^2+5t-3}[/tex]simplify the first term
[tex]\frac{5}{9-24t^{}}=\frac{5}{3(3-8t)^{}}=-\frac{5}{3(8t-3)^{}}[/tex]simplify the second term
[tex]\frac{3t-2}{8t^2+5t-3}=\frac{3t-2}{8(t+1)(t-0.375)}=\frac{3t-2}{(t+1)(8t-3)}[/tex]the LCD is equal to
-3(t+1)(8t-3)option Aa conference hall has 33 rows of seat. the last row contains 80 seats if each row has two fewer seats than the row behind it, how many seats are there in the first row?a.20b.18c.16d.14
Given:
A conference hall has 33 rows of seat,the last row contains 80 seats if each row has two fewer seats than the row behind it.
There will be, 16 numbers of seats in the first row.
au =- 10 + 4(11 - 1) Question (pregunta) Answer (respuesta) What is the first term? What is the common difference? What term are you calculating?
au = -10 + 4(11 - 1)
Ok
The first term is -10
What is the common difference (11 - 1)
What term are you calculating? 11 - (-10) = 11 + 10 = 21
Which of the following statements are true, given Angle S cong to angle J and angle N cong to angle E?
Given,
[tex]\begin{gathered} \angle S\cong\angle J \\ \angle N\cong\angle E \end{gathered}[/tex]When two angle of the angles are equal then the remaining third angle is also equal.
Beacuase the sum of the interior angle of triangle is 180 degree.
It make the third angle also equal.
Hence, angle A is congurent to angle O.
Statement 1 is true.
In the second statement,
when two triangle all its angles congurent then triangles are similar.
Statement 2 is true.
In the third statement,
If the angles are equal then it can be possible that sides are equal or not equal.
If the sides of the triangle are not congruent then triangle cannot be congruent.
Statement 3 is not true.
In the forth statement,
similar to the third statement, sides of the triangle can be congurent or not.
Statement 4 is false.
In the fifth statement,
The triangle are similar then its perimeter can be equal or half or in other fraction to each other.
Statement 5 is false.
Similarly, statement 6 ia true.As the angles are equal so the traingles can mapped onto.
Statement 7 is true.
For the following function, find the value of (a) f(−1) and (b) f(1), if possible.y= 2 if x≤09 if x>0
Given:
The function is,
[tex]\begin{gathered} y=2\text{ if x}\leq0 \\ =9\text{ ifx>0} \end{gathered}[/tex]The value of function at x = -1 is,
[tex]\begin{gathered} \text{For x=-1,} \\ f(x)=y=2,\text{ if x}\leq0 \\ f(-1)=2 \end{gathered}[/tex]And,
[tex]\begin{gathered} \text{For x=1,} \\ f(x)=y=9,\text{ if x>0} \\ f(1)=9 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} f(-1)=2 \\ f(1)=9 \end{gathered}[/tex]Please help me :((Find the slope of the line below. Enter your answer as a fraction or decimal.Use a slash mark (/) as the fraction bar if necessary.10(7,3)(-8, 0)1010
Given two points on a line, we can find the slope of the line using the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]then, in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,0) \\ (x_2,y_2)=(7,3) \\ \Rightarrow m=\frac{3-0}{7-(-8)}=\frac{3}{7+8}=\frac{3}{15}=\frac{1}{5} \\ m=\frac{1}{5} \end{gathered}[/tex]therefore, the slope of the line is m = 1/5
if you reflect point “Y” on the line y=2, what coordinate point (c,y) do you get?
Assume that the coordinates of point Y are (x,y)
see the figure below to better understand the problem
The coordinates of the image of point Y are (x,4-y)
Which of the following equations is equivalent to the logarithmic equationbelow?x = In4
A natural logarithm expression ln(x) = y can be rewritten as
[tex]\begin{gathered} \ln (x)=y \\ e^y=x \end{gathered}[/tex]Hence, for an expression
[tex]\ln (4)=x[/tex]This can be rewritten as
[tex]e^x=4[/tex]The answer to this problem is option D, which corresponds to the equation written above.
PLEASE HELP NO.13 GIVING BRAINLIEST
Answer:
329 Dalmatians remaining
Step-by-step explanation:
To have 6 times as many Dalmatians of one coloration as of the other, the total must be a multiple of 7.
In order to be able to give away an integer number that is 6% of the total, the total must be a multiple of 50.
The least common multiple of 50 and 7 is 350.
94% of 350 is 329
So there are 329 Dalmatians remaining!
Hope this helps! :)
The amount of money earned on a job is directly proportional to the number of hours worked. If $36 is earned for 8 hours of work, how much is earned for 30 hours of work?Answers:150$96$135$
the relationship between money earned and the working hour is proportional,
so,
let money = m
and hours = h
[tex]undefined[/tex]how much water should be added to 110 oz. of 60% acid solution to dilute it to a 45% acid solution? round answer to the nearest hundredth if necessary
We are given the following information:
110 oz of 60% acid solution
We need to find the amount of water needed to dilute it to 45%.
To answer this, let's set up the equation first.
We know that 60% of the 110 oz. is acid. This amount of acid must then be the same amount of acid that makes up 45% of the new solution. So our equation would be:
[tex]60\%\times110=45\%\times N[/tex]Solving for N, we get:
[tex]\begin{gathered} 0.60(110)=0.45N \\ 66=0.45N \\ \frac{66}{0.45}=N \\ \\ N=146.666...\approx146.67 \end{gathered}[/tex]Now we know that the total amount must be 146.67 oz. We already have 110 oz. So we only need 146.67 - 110 = 36.67 oz of water to dilute the solution.
If the leading coefficient of a polynomial function is positive, the graph will go
blank1 to the right. If the leading coefficient of a polynomial function is negative, the graph will go blank2 to the right.
Step-by-step explanation:
the leading coefficient means the coefficient (factor) of the term with the highest exponent of the variable (typically x).
with sufficiently large values of this variable (x - going far enough to the right) this term will "win" in value against any other term of the polynomial expression.
and therefore the sign of its factor (coefficient) will determine, if the curve will go up or down.
a positive factor (coefficient) will make the value of this term and therefore of the whole polynomial larger and larger, making the curve going up to +infinity.
a negative factor (coefficient) will make the value of this term and therefore of the whole polynomial smaller and smaller (more negative and more negative), making the curve going down to -infinity.
Your rich playful uncle makes you a proposition. he says hell give you 1000 if you cqn tell him how much money each of the following options would make.He’ll give you 10000 to deposit in a account. The account pays a 3.5% Interest compounded at the end of each year. You get to keep the amount of money in the bank at the end of the 15th year. He’ll give you one dollar the first day, two dollars the second, and three dollars the third. So on and so on, for the next 15 years. Which is a better option? Explain your answer or your uncle won’t give you your money.
The first option :
10000 to deposit in a account.
The account pays a 3.5% Interest compounded at the end of each year.
We need to find the money at the end of 15th year
So, P = 10,000 , r = 3.5% = 0.035 , t = 15 years
so,
[tex]\begin{gathered} A=P\cdot(1+r)^t=10000\cdot(1+0.035)^{15} \\ A=10000\cdot1.035^{15}=16,753.5^{}^{}_{}^{} \end{gathered}[/tex]The second option:
He’ll give you one dollar the first day, two dollars the second, and three dollars the third. So on and so on, for the next 15 years.
So, it will represent an arithmetic sequence : 1 , 2 , 3 , ..... and so on
the first term = a = 1 , the common difference = d = 1
So, the rule of the sequence will be:
[tex]A(n)=a+d(n-1)[/tex]The number of days of the year = 365
So, for 15 years
The number of days = 15 * 365 = 5,475 days
So, we need to find the sum of the sequence for 15 years
at the last day of 15 years , he will give him:
[tex]1+1\cdot(5475-1)=5,475[/tex]So, the sum will be:
[tex]n\cdot\frac{a1+an}{2}=5475\cdot\frac{1+5475}{2}=5475\cdot2738=14,990,550[/tex]So, the better option is the second
4. The following table is proportional. Complete the table below and SHOW YOUR WORK!!xyk=y/x107085653521412What is the equation of the table above?____
Where:
k = Constant of proportionality
Using the values from the table:
[tex]\begin{gathered} x=10,y=70 \\ 70=10k \\ so\colon \\ k=\frac{70}{10} \\ k=7 \end{gathered}[/tex]Therefore, the equation for the table is:
[tex]y=7x[/tex]Find the unit price.Find which is the better buy (lower cost per ounce) by finding each unit 6) price rounded to three decimal places if necessary. Assume that different sizes of the same brand are being compared. Frozen orange juice: $11.86 for 18 ounces $7.80 for 12 ounces
To determine the better bargain of the two items, we shall calculate the unit price as follows;
[tex]\begin{gathered} \text{For 18 ounces;} \\ \text{Unit price}=\frac{11.86}{18} \\ \text{Unit price}=0.6588 \\ \text{Rounded to 3 decimal places;} \\ \text{Unit price}=0.659 \end{gathered}[/tex][tex]\begin{gathered} \text{For 12 ounces;} \\ \text{Unit price}=\frac{7.80}{12} \\ \text{Unit price}=0.65 \end{gathered}[/tex]The unit price for both categories are given. From our calculations, we can determine that $7.80 for 12 ounces is a better deal because, this costs less as compared to the other one. The difference is insignificant but nevertheless, there is a difference between $0.659 and $0.650
ANSWER:
The better buy is $7.80 for 12 ounces
Factore each trinomial. If the trinomial cannot be factored, write, prime.1) x^2+10x+92) x^2-6x-273) x^2+14x-32
The factors of 9 that sum to 10 are 9 and 1, so:
[tex]x^2+10x+9=(x+1)(x+9)[/tex]2)
[tex]x^2-6x-27[/tex]The factors of -27 that sum to -6 are 3 and -9, so:
[tex]x^2-6x-27=(x+3)(x-9)[/tex]3)
[tex]x^2+14x-32[/tex]The factors of -32 that sum to 14 are 16 and -2, so:
[tex]x^2+14x-32=(x+16)(x-2)[/tex]Given thetha , a positive angle less than 2pi, fill out each of the following in terms of theth.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
angle θ: < 2π
positive
Step 02:
We must use the Cartesian plane and the reference angles to fill the table.
Table
θ in QI θ in QII θ in QIII θ in QIV
reference angle θ π - θ θ - π 2π - θ
sin-1 (sin θ) θ
cos-1 (cos θ) θ
θ in QI :
θ
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = angle
= θ
θ in QII :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = 180 - angle
= π - angle
= π - θ
θ in QIII :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = angle - 180
= θ - π
θ in QIV :
sin-1 (sin θ) = θ
cos-1 (cos θ) = θ
reference angle = 360 - angle
= 2π - θ
That is the solution.
On a unit circle, the terminal point of 0 is (0, -1). What is tan 0?
Answer:
Undefined
[tex]\tan \theta=\text{ undefined}[/tex]Explanation:
Given that the terminal point on a unit circle is at;
[tex](0,-1)[/tex]Recall that from trigonometry tangent is;
[tex]\tan \theta=\frac{opposite}{adjacent}=\frac{y}{x}=\frac{-1}{0}[/tex]and we know that any number divided by zero is undefined.
Therefore;
[tex]\tan \theta=\text{ undefined}[/tex]tan theta = undefined
Suppose you have an income of $100 perweek. Draw a circle graph to show howyou would use the money. Include at least4 categories Hurry up
Given
You earn $100 per week, now draw circle graph on you would use the $100Include at least 4 categories
Solution
Key note
A for clothes
B for Transport fare
C for Food
D for Gift to the needy
E for Grocery
The probability that Nicole will be employed in her field of study following college graduation is 0.82.What is the complement, the probability that she will not be employed in her field of study following college graduation?
ANSWER
0.18
EXPLANATION
We have that the probability that Nicole will be employed in her field of study following College graduation is 0.82.
The complement of a probability is the probability that an event will not take place. We can find it by subtracting the probability that an event will take place from 1:
P' = 1 - P
Therefore, we have that the probability that she will not be employed in her field of study following college graduation is:
P' = 1 - 0.82
=> P' = 0.18
That is the answer.
A toy rocket is launched from a platform 39 ft above the ground..... How high will the rocket be after 3 seconds?
In order to calculate the rocket's height after 3 seconds, let's use t = 3 in the equation and calculate the value of the expression:
[tex]\begin{gathered} h=-16t^2+83t+39\\ \\ h=-16\cdot3^2+83\operatorname{\cdot}3+39\\ \\ h=-16\operatorname{\cdot}9+249+39\\ \\ h=-144+288\\ \\ h=144\text{ ft} \end{gathered}[/tex]Therefore the correct option is the first one.
Decide whether the following is observational study, experimental, survey or none of the above: The manager of a grocery store wants to know if a product’s location in the store affects how well the product sells. He first tracks how many of a certain item sells over a month when the display is located where it always has been. He then moves the display to the front of the store so customers see it when they first enter. He again tracks how many of the items sell over a month and compares the numbers. a) experimental b) none of the above c) survey d) observational study
Step 1
An observational study is a study in which the researcher simply observes the subjects without interfering. That is, the researcher has no control over any treatments the subjects may be given or which groups the subjects may be separated into, etc.
A survey experiment is an experiment conducted within a survey. In an experiment, a researcher randomly assigns participants to at least two experimental conditions. The researcher then treats each condition differently.
A survey is an investigation of the characteristics of a given population by means of collecting data from a sample of that population and estimating their characteristics through the systematic use of a statistical methodology.
Comparing the definitions above to the question given, the answer will be;
[tex]Observational\text{ study}[/tex]