4. Angle X in the triangle below is a right angle.
W
15
X
T
h
-25-
2
20
R
9²4625
9+ 25²..
= 20²
400
-625-625
19² √225
15
(a) What is the measure of angle W?
450
(b) What is the height, h, of the triangle?
15.
/2 pts)
Answers
a ) The required measure of x = 90°
b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]
Given is a triangle with measure 15, 20 and 25
a ) Since a perpendicular is dropped from above
the two angles of x are equal because the angle is bisected by an angle bisector
So to check whether the angle x is a right angled or not
we can use the pythagoras theorem and check if the LHS = RHS or not
LHS = 15² + 20² = 225 + 400 = 625
and RHS = 25² = 625
Since LHS = RHS thus the angle is 90 degrees
b ) The height of the right triangle ;
by using the Pythagoras theorem again
12.5² + h² = 20² { side 25 is bisected = 12.5 }
h² = 400 - 156.25
h = [tex]\sqrt{244}[/tex]
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Related Questions
Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answers
Answer: 324
Step-by-step explanation: 10% is the same as 1/10
360/10 is 36
360-36= 324
meaning 324 students now attend Haley elementary school <3
hope this helps <33
On a coordinate plane, the position of two friends can be defined by the points A(1,3) and B(7,6). Their teacher is standing at point C, the teacher’s distance from point A is twice the distance from Point B. What are the coordinates of point C?
A.) (5,5)
B.) (-5,5)
C.) (4, 9/2)
D.) (8/3, 3)
Please show work if possible!
Answers
The coordinate of point C will be (5, 5). Then the correct option is A.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.
The ratio is given as 2:1.
x = (7 × 2 + 1 × 1) / (2 + 1)
x = 15 / 3
x = 5
y = (6 × 2 + 1 × 3) / (2 + 1)
y = 15 / 3
y = 5
The coordinate of point C will be (5, 5). Then the correct option is A.
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A store pays $114 for a picnic table. The store marks up the price by 28%. What is the
amount of the mark-up?
Answers
The markup price on the table would be $32.
What is the markup price?The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %. The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.So, we have:
Discount = 28%The selling price of the picnic table = is $114Now, calculate the makeup price:
Mark-up price = Discount * Selling Price
Mark-up price = (28/100) * 114
Mark-up price = 31.92
Mark-up price ≈ 32.
Hence, the markup price on the table would be $32.
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(2 points) Let x³ - 2x²-x+2=0 be a polynomial equation. Find the list of all potential rational solution(s) for the polynomial equation using the
Rational Root Theorem. Then, find the actual rational solution(s).
1. Find all potential rational solution(s).
Answer (separate by commas):
2. Find all distinct actual rational solution(s).
Answer (separate by commas):
Note: You can earn partial credit on this pmblem
Answers
Potential rational solution(s) to the above polynomial equation is ±1, ±2.
Actual rational solution are ±1, +2.
What is polynomial equation?
Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.
Main Body:
Given:
x³ - 2x² - x +2 = 0
We will use the Rational Root Theorem:
If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.
So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:
±1,±2
Dividing x³ - 2x² - x +2 = 0 by x-1, we get
x²-x-2 as quotient.
Splitting the middle term ,
⇒x² - 2x + x - 2
⇒x(x- 2) + 1(x-2)
⇒(x+1)(x-2)
so x= -1 , 2
Hence the rational solution to the equation are ±1, 2.
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find the standard form of the equation of the circle with end points of a diameter at the point (2,3) and (-5,5)
Answers
Mr. Olin bought 6 sketchbooks for the students in his art class. Each sketchbook was on sale for $3 oG. If the sketchbooks cost $18 total before tax, what was the original price of each sketchbook
Answers
Answer:
i think it is 18
Step-by-step explanation:
because if he brought 6 for $18 and it was in sale for $3 that means there is no tax
Whats the answer please
Answers
The domain of the given function f(x) = (-x - 9)^(1/2) is; C) (-∞, -9)
What is the domain of the function?The domain of a function is defined as the set of all possible input values that make the function possible.
Now, we are given the function;
f(x) = (-x - 9)^(1/2)
This can also be written as;
f(x) = √(-x - 9)
Now, since the item in bracket seems to be negative, we can say that we want to find the lowest term for which the function in bracket is zero because when the function in the bracket is negative, then the function is a complex number. Thus;
At (-x - 9) = 0
-x = 9
x = -9
This will be the maximum value of x while the minimum value will be negative infinity.
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The average December temperature in Salt Lake City, Utah is 10 degrees Farenheit. The actual December
temperture can vary in Salt Lake City by 5 degrees Farenheit either above or below the average. What is the
minimum temperature of Salt Lake City in December?
Answers
The minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
The average December temperature in Salt Lake City, Utah, is 10 degrees Fahrenheit. The actual December temperature can vary in Salt Lake City by 5 degrees Fahrenheit either above or below the average.
We need to find out the minimum temperature in Salt Lake City in December. Let the temperature be denoted by the variable "M". The minimum temperature is the difference between the average temperature and the variation in the temperature.
M = 10 - 5
M = 5
Hence, the minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
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HELPP ME PLEASEEEEEE
Answers
Answer:
We can see that as x increases, y decreases. This indicates a negative slope meaning that the two variables are negatively related.
Hope this helps! :)
The daily production costs for a golf ball manufacturer can be modeled with the function C(x) = 0.1x2 - 7x + 140, where C(x) is the total cost and x is the number of golf balls produced per hour. Use the graph to answer the question.
Graph of function c of x equals 0 point 1 x squared minus 7 x plus 140. The graph has the axis labeled as number of golf balls produced, and the y-axis labeled as cost. The curve begins at (0, 140), decreases to (35, 17.5), and then increases to infinity.
Which statement shows the correct relationship between production cost and number of golf balls produced?
Answers
The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Then the minimum is represented by the formula;
c - b² / 4a
We have given equation C(x) = 0.1x² - 7x + 140
a = 0.1
b = -7
c = 140
Now plugging in values to c - b² / 2a
= 140 - 7² / (4 * 0.1)
= 17.5
The minimum production cost will be; 17.5
Now plugging 35 into the given equation;
C(x) = 0.1x² - 7x + 140
C(x) = 0.1 ( 35)² - 7 (35) + 140
C(x) = 17.5
Therefore, 35 golf balls produce the minimum cost.
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Answer:
that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
Step-by-step explanation:
Two rockets are to be launched at the same time from NASA headquarters in Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 19,200 miles per hour and the second rocket will travel at 18,000 miles per hour. If the first rocket is scheduled to reach the space station 0.5 of an hour before the second rocket, how far is the space station from NASA headquarters?
Answers
By solving a linear equation, it can be calculated that
The space station is at a distance of 144000 miles from NASA headquarters
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let the space station be d miles from NASA headquarters
Speed of the first rocket = 19200 miles/hour
Speed of the second rocket = 18000 miles /hour
Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]
Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]
By the problem,
[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]
The space station is at a distance of 144000 miles from NASA headquarters
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Use the following model to answer the question.
3 groups are shown. Each group shows 2 tens rods and 6 ones cubes.
Which division problem is shown by the model?
Which division problem is shown by the model?
Which division problem is shown by the model?
A.
0
.
66
÷
3
=
0
.
22
B.
0
.
66
÷
3
=
0
.
26
C.
0
.
78
÷
3
=
0
.
62
D.
0
.
78
÷
3
=
0
.
26
Answers
Answer: 78 ÷ 3 = 26
Step-by-step explanation:
We are given that there are 3 groups shown. This means we will be dividing by 3.
We are given that each group has 2 ten rods (20) and 6 ones cubes (6). This means the answer is 26.
Lastly, 26 * 3 = 78, meaning we are dividing 78 by 3.
This gives us:
78 ÷ 3 = 26
Determine the period.
2 y
-2
1
10
Answers
Answer:
8
Step-by-step explanation:
You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.
PeriodThe period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.
Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:
period = 9 - 1 = 8
The period of the function is 8 units.
__
Additional comment
In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).
Identify the values of the variables. Give your answers in simplest radical form. Help!
Answers
Considering the triangle given the variables are calculated to be
x = (5√6)/3
y = (10√6) / 3
How to calculate the unknown variablesInformation given in the question
right angle triangle
The unknown variables is calculated using SOH CAH TOA
Definition of variables for the right angle triangle
hypotenuse = y
opposite = 5√2
adjacent = x
The variable x is solved using tan, TOA, the angle is 60
tan 60 = Opposite / Adjacent
tan 60 = (5√2) / x
x = (5√2) / tan 60
x = (5√6)/3
The variable y is solved using sin, SOH, the angle is 60
sin 60 = Opposite / Hypotenuse
sin 60 = (5√2) / y
y = (5√2) / sin 60
y = (10√6) / 3
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there are 4 consecutive even integers that sum to 276
Answers
The required consecutive even integers are 66, 68, 70, and 72.
We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.
Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".
S = n + (n + 2) + (n + 4) + (n + 6)
276 = 4n + 12
4n = 264
n = 66
Hence, the required integers are 66, 68, 70, and 72.
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A house on the market was valued at $355,000 . After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answers
Answer: $323,050
Step-by-step explanation:
355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)
355,000- 31,950 = 323,050 which is your answer, hope this helped <3
Mike Meier purchased a lawnmower for $328.61, a lawn sprinkler for $13.27, and a hose reel for $27.96. He must pay the state tax of 5.5 percent, the county tax of 1.5 percent, and the city tax of 2 percent. What is the total purchase price?
Answers
Answer: $402
Step-by-step explanation: I believe this answer is correct i did all the math
When Nathaniel moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 38 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Answers
The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6
The equations of the growth of both treesFrom the question, we have the following parameters that can be used in our computation:
Tree A
Initial height = 38 inchesRate = 6 inches each yearTree B
Initial height = 20 inchesRate = 9 inches each yearThe height after t years is
Tree = Initial height + rate * t
So, we have
Tree A = 38 + 6t
Tree B = 20 + 9t
The interval of timeRecall that
Tree A = 38 + 6t
Tree B = 20 + 9t
When Tree A is taller than Tree B, we have
38 + 6t > 20 + 9t
Evaluate the like terms
-3t > -18
Divide
t < 6
Hence, the interval is t < 6
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The data to the right represent the cost of living for 20
states. The cost of living is a measure of the average
price paid for housing, utilities, groceries, healthcare,
transportation, and miscellaneous expenses. The
national average cost of living is 100. The data can be
used to compare a state to the national average and
to other states.
T
Use these data to construct a frequency distribution with a first class of 85.0-94.9. Fill in the missing classes and the frequency for each class belo
Cost of living
Number of states
9
85.0-94.9
125.0134.9
8-8
20
(Type integers or decimals. Do not round.)
151.2121.3 99.4 94.5 89.7
138.7120.1 96.7 94.5 89.6
132.1106.5 95.3 90.9 89.4
124.9101.6 95.2 90.1 89.2
Answers
The frequency distribution based on the information given is illustrated below.
What is the frequency distribution of table?
A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.
It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
Given the above information the frequency distribution table is:
Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex] Number of states
85.0 - 94.9 9
95.0 - 104.9 5
105.0 - 114.9 0
115.0 - 124.9 2
125.0 - 134.9 2
135.0 - 144.9 1
145.0 - 154.9 1
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0.8421 as a fraction
Answers
Answer:
8421/10000
Step-by-step explanation:
8421/10000
A letter is chosen at random from the word MATHEMATICS. Find the probability that it will be
a) an H
b) an M
c) a B
d) a vowel,
e) a letter other than an A
Answers
Answer:
a) 1/11
b) 2/11
c) 0/11
d) 4/11
e) 9/11
Step-by-step explanation:
'MATHEMATICS' has 11 letters.
a) there is only one H out of the 11 letters meaning the probability is 1/11
b) there are two M s out of the 11 letters meaning the probability is 2/11
c) there is no B in the word meaning the probability is 0/11
d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11
e) there two A s in the word and 11-2=9 meaning the probability is 9/11
Hope this helps :)
Please Help
Find(f+g)(x)if f(x)-/16x4 and g(x)=3x2-3x-5
Answers
The function operation (f + g)(x) of the functions f(x) = √( 16x⁴ ) and g(x) = 3x² - 3x - 5 is -5x² + 5x - 7.
What is the function operation (f + g)(x) of the given functions?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( 16x⁴ )g(x) = 3x² - 3x - 5To determine the function operation (f + g)(x), replace the function designators with the functions and simplify.
(f + g)(x) = f(x) + g(x)
(f + g)(x) = √( 16x⁴ ) + ( 3x² - 3x - 5 )
Replace √( 16x⁴ ) with 4x²
(f + g)(x) = 4x² + 3x² - 3x - 5
Collect and add like terms
(f + g)(x) = 7x² - 3x - 5
Therefore, the function operation (f + g)(x) is 7x² - 3x - 5.
Option A is the correct answer.
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Subtract the linear expressions. Show your work.
(4-3x + 9x) - (-11-7x + 9)
Answers
First distribute the negative (-1) outside of the parentheses to each term inside of the parentheses. In each linear expression there are like terms: those with variable x and constants. These can be combined (I.e., added or subtracted from one another).
Here’s a photo of the work used to simplify the expression. I hope it helps:
How you find interest rates
Answers
Most often, borrowers receive their interest rates as an annual percentage. It can be beneficial to translate this rate into a monthly percentage to better understand how the interest affects your loan payments. Here is a list of steps you can follow to help you discover your monthly interest rate:
example:
1) Convert percentage to a decimal: The first step is to take the annual rate percentage and convert it into a decimal by dividing the number by 100. For example, if your annual interest rate is 15%, dividing 15 by 100 would equal 0.15.
2)Divide by 12: Next, divide the translated percentage by 12, the number of months in one year. If your translated percentage was 0.15, dividing that number by 12 would equal 0.0125.
3)Multiply by the value of the asset: Multiplying your calculated amount by the value of the asset or loan, allows you to see how much extra money is being added to your loan payments every month. Using the previous value of 0.0125, if you took out a loan of $5,000, the calculation would be 0.0125 x 5,000 = 62.5. This means that every month, your interest rate adds $62.50 to your loan payments.
Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. What is the current price of the bonds?
b. By what percent will the price of the bonds increase between now and maturity? (Round "PV Factor" to 3 decimal places, intermediate and final answers to 2 decimal places. Omit the "%" sign in your response.) Price increases by %
Answers
a) The current bond price (present value) is $420.03.
b) The percentage by which the price of bonds will increase between now (current) and maturity (18 years) is 138%.
How is the bond price determined?The current bond price represents its present value.
The present value is the discounted future cash inflows.
We can compute the present value using an online finance calculator as follows:
N (# of periods) = 18 years
I/Y (Interest per year) = 12$
PMT (Periodic Payment) = $40 ($1,000 x 4%)
FV (Future Value) = $1,000
Results:
PV = $420.03
Sum of all periodic payments = $720.00
Total Interest = $1,299.97
Percentage increase in bond price = [(Future value - Present value)/Present value x 100]
= 138% [($1,000 - $420.03)/$420.03 x 100]
Thus, the present value of the bonds $420.03 will grow by 138% at maturity.
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List 1 4/5, -7/4, 41%, and -1.3 from greatest to least.
Answers
The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.
What us descending order?
When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.
Main Body:
To solve this question we need to convert all numbers into decimal system.
calculate:
1 can be written as 1.00
4/5 can be written as 0.8
-7/4 = -1.75
41% = 41/100 = 0.41
-1.3 can remain as it is because it itself is in decimal form.
Hence the order from greatest to smallest is as
1 > 0.8 > 0.41 > -1.3 > -1.75
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find the value of the ratio (red to blue) of the areas of the similar figures. Write the ratio as a fraction in simplest form. 12 and 8
Answers
The ratio of the areas of the similar figures is given as follows:
225/16.
What are similar figures?Similar figures are figures that share these two features:
Congruent angle measures, that is, the same angle measures.Proportional side lengths.The ratio of the side lengths of the similar figures can be represented as follows:
(b/a).
The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:
(b/a)² = b²/a².
From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:
15/4.
Hence the ratio of the areas of the figures is given as follows:
(15/4)² = 225/16.
Missing InformationThe figures are given by the image at the end of the answer.
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screenshot included with question
Answers
Answer:
48 fl oz = 6 c
4 gal = 16 qt
Step-by-step explanation:
4 times 4 is 16
48 divided by 8 is 6
4 gal = 16 qt as 4x4 is 16!
4. Solve for y.
q
116° +15y - 4=180
Answers
After simplifying the expression, the value of y is 4.53.
In the given question,
We have to solve for y.
The given expression is 116° +15y - 4=180.
To solve for y we simplify the expression.
The expression is 116° +15y - 4=180
Now simplifying the expression.
Add 4 on both side
116° +15y - 4+4=180+4
116° +15y=184
Subtract 116 on both side
116° +15y-116°=184-116°
Simplifying
15y=184-116°
15y = 68
Divide by 15 on both side
15/15 y=68/15
y=4.53
Hence, the value of y is 4.53.
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20 points Describe another way you could have solved the equation. Tell which of these two ways of solving the equation you prefer and why.
Answers
In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450
EquationsEquations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
To solve for m, we have to expand the bracket and make m the subject of formula.
2[(4m * 3.5) / 400] = 171.5
2[14m/400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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