Answers
Consider that there are, generally, the following types of angles pairs,
1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.
2. Complementary Angles: Angles that are adjacent and together form a right angle.
3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.
a.
The adjacent angles to angle 4 are angles 1 and 3.
There are no complementary angles associated with angle 4.
The supplementary angles to angle 4, are angles 1 and 3.
Thus, the angle pairs that include angle 4 are,
[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.
The adjacent angles to angle 5 are angles 6 and 7.
There are no complementary angles associated with angle 5.
The supplementary angles to angle 5, are angles 6 and 7.
Thus, the angle pairs involving angle 5 are,
[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]Related Questions
An investment firm invested in two companies last year. They invested $12,000 in Company A and made a profit of 14%. They
invested $8000 in Company B and made a profit of 21%.
Answer the questions below. Do not do any rounding.
(a) What was the investment firm's total profit?
$0
(b) What was the percent profit for their total investment?
Answers
The investment firm's total profit is $ 3360 and the percent profit for their total investment is 16.8%.
How to calculate percentage of a situation?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
Formula for percentages: (Value/Total value) * 100
Given, amount invested in company A = $ 12,000
Amount invested in company B = $ 8000
Profit earned by company A = 14%
Profit earned by company B = 21%
Amount in profit earned from company A = (12000*14)/100 = $ 1680
Amount in profit earned from company B = (8000*21)/100 = $ 1680
Therefore total profit of the investment firm = $ (1680 + 1680) = $ 3360
Thus, the investment firm's total profit is $ 3360.
Now, percentage profit of total investment = (3360/20000)*100 = 16.8%, using available literature and formula.
Thus, the percent profit for their total investment is 16.8%
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find the derivative of [tex]\sqrt({x^{2}*6^x})^9[/tex]
Answers
Answer: [tex]9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
Step-by-step explanation:
[tex]w=\sqrt{(x^2 6^x)^9}=(x^2 6^x)^{9/2}=x^9 6^{9x/2}\\\\[/tex]
Using the product rule,
[tex]\frac{dw}{dx}=6^{9x/2}\frac{d}{dx} (x^9)+x^9 \frac{d}{dx}(6^{9x/2})\\\\=9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]
Find y when x = 1, if y = 3 when x = 2. a. y = x; y =  b. y = –x; y = – c. y = x; y =  d. y = x; y = 1
Answers
ANSWER
y = 1.5 or 3/2
EXPLANATION
We are given that:
y = 3 when x = 2
From the question, we know that y and x have a proportional relationship.
This means that y and x change at the same rate:
=> y = kx
where k = constant of proportionality
y is 3 when x is 2:
3 = k * 2
=> k = 3/2 = 1.5
Therefore, when x = 1:
y = 1.5 * 1
y = 1.5 or 3/2
find z and y..no decimals just exact answers
Answers
Triangle is a right triangle because has a 90° angle
then we can use trigonometric ratios to find sides
if I use sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]whre alpha is the reference angle, O the opposite side to the angle and h the hypotenuse of the triangle
using 60° as reference angle
[tex]\sin (60)=\frac{x}{4\sqrt[]{3}}[/tex]then solve for x
[tex]\begin{gathered} x=4\sqrt[]{3}\sin (60) \\ \\ x=6 \end{gathered}[/tex]the value of side x is 6 units
If I use cosine
[tex]\cos (\alpha)=\frac{A}{H}[/tex]where alpha is the reference angle, a the adjacent side to the references angle and H the hypotenyse of the triangle
using 60° as reference angle
[tex]\cos (60)=\frac{y}{4\sqrt[]{3}}[/tex]then solve for y
[tex]\begin{gathered} y=4\sqrt[]{3}\cos (60) \\ \\ y=2\sqrt[]{3} \end{gathered}[/tex]the value of side x is 2root3 units
A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.Enter the answer
Answers
Let's define,
X := Total minutes it takes to fill the plane (with fuel)
Then,
[tex]X\cdot0.20=12.40[/tex]Solving it for X, we get
[tex]X=\frac{12.40}{0.20}=62\text{ min}[/tex]This means that the vehicle takes 1 h 2 min to fill the plane. If the fuelling finished at 10:35, it began at
[tex]10-1\colon35-2=9\colon33[/tex]9:33.
An electronics store has portable CD players on sale for $54.95.If the local sales tax is 6.5%, what is the total cost of a CD player?
Answers
The total cost of a CD player is $58.52
Name three real-world applications of polynomials and why they impact society.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
polynomials
Step 02:
applications of polynomials:
The polynomials can be represented graphically, and are used in many economics and engineering problems. In economics they appear, for example, to model markets, showing how prices vary over time; how raising or lowering the price of a product affects its sales; or also in the calculation of taxes.
In forestry engineering, for example, we need geometry to calculate areas, but also polynomials in problems such as calculating how many trees we need to replant after having cut down an area of a forest.
Other uses of polynomials are the calculation of the trajectory of projectiles (they are parabolic trajectories), or in the calculation of orbits of satellites or rockets.
That is the full solution.
please help. I don't understand this
Answers
The answer of the expression is 3 -4 and the sum is -1
Given,
In the figure, given a number line.
And, write an addition expression represented by number line. Then find the sum.
Now, According to the question:
To solve for an expression is:
Calculate the principle based on the number line .
We can figure out the formula .
= 3 - 4
[Moving to the right is positive and moving to the left is negative ]
To find the sum:
3 - 4 = -1
According to the figure , the end point of the movement is -1 and the answer is correct.
Hence, The answer of the expression is 3 -4 and the sum is -1
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The sum of a number and five more than the number is 17.
Answers
The number is 6.
What is a number?
A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
Let the number be n.
Then according to que, n + (5+n) = 17
or, 2n = 17 - 5
or, n = 12/2 = 6
Hence the number is 6.
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Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2
Answers
Given: The following
[tex]\begin{gathered} N_{umber\text{ of faces}}=7 \\ N_{umber\text{ of vertices}}=10 \end{gathered}[/tex]To Determine: The number of edges
Solution:
The Euler's formula is given as
F + V = E + 2,
where F is the number of faces,
V the number of vertices, and
E the number of edges.
Substitute the given into the formula
[tex]\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}[/tex][tex]\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}[/tex]Hence, the number of edges possessed by the polyhedron is 15
Kristin has to pick up her children, who all attend different schools. She is at home (H) and needs to go to children First Pre-School (C), Braden Rivera Elementary (B) and stephen middle school (S). Kristin estimates the distance among these locations as follows. H to C is 5 miles. H to B is 8 miles. H to S is 15 miles. C to B is 11 miles, C to S is 17 and B to S is 10 miles..What is the minimum distance Kristin can travel?
Answers
In order to find the minimum distance, first let's write a map with all positions and distances:
Now, let's write the total distance for the paths she can choose:
[tex]\begin{gathered} HBCS=8+11+17=36 \\ HBSC=8+10+17=35 \\ HCBS=5+11+10=26 \\ HCSB=5+17+10=32 \\ HSBC=15+10+11=36 \\ HSCB=15+17+11=43 \end{gathered}[/tex]Therefore the minimum distance is 26 miles.
Lin needs to mix paint ratio 3 cups yellow to 2 cups red.how many cups of red and yellow do you need to get 20 total cups of paint
Answers
Mix of paintings to obtain 20 cups of paint
there are 3X cups of yellow
there are 2Y cups of red
then find X and Y such that
3X + 2Y = 20
One possible solution is X = 2 Y= 7
2 cups yellow, and 7 cups red
hello i have a upcoming test and want to know how to solve this
Answers
Expression given:
[tex]g>1[/tex]To know how to graph the given expression, it is easier if we determine what it means in words. In this case, this expression means all the values above one (without including one).
We know that one is not included as it has the sing ">", if the value were included, then it would have the sing "≥" or "≤".
This is important because when you are graphing, a discontinuous line is drawn for values not included, and a continuous one for included values.
Now, we would have to evaluate if it is the independent variable (generally called x), or the dependent variable (generally called y).
Assuming that g is the dependent variable, then the graph would be like this:
However, if the variable was de independent variable, then it would look like this:
We have to note that both graphs go from 1 to bigger values.
In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 12% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 176 milliliters of pure alcohol?
Answers
Answer:
700 ml of Solution B was used
Step-by-step explanation:
Whenever we have unknowns the first thing to do is to represent the unknowns using variables, set up equations using given information and solve equations for the unknowns
Here the unknowns are volume of solution A and volume of solution B
Set up our variables as follows
Let x = volume of solution A used for mixing in ml
Let y = volume of solution B used for mixing in ml
We are given that volume of A used is 400 ml less than volume of B used
In math terms this can be represented as
y - x = 400
Or,
- x + y = 400 [1]
We are given the percentages of alcohol in A and B respectively
Since A contains 12% alcohol, the actual volume of alcohol in A
= 12% of x ml
= 0.12x (12% = 12/100 = 0.12)
Similarly alcohol by volume in B
= 0.20x
Total alcohol by volume if x of A and y of B are mixed is
0.12x + 0.20y
and we are given that this quantity is 176 ml
So we set up our second equation as
0.12x + 0.20y = 176 [2]
Using both equations we eliminate either the x or y terms to arrive at an equation involving only the other term.
Since the question asks us to determine only the volume of Solution B used, we should eliminate x term from both equations to get a single equation involving only the y term
Let's review the equations:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
Make the coefficients of x the same :
Multiply [1] by 0.12
=> -0.12x + 0.12y = = 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
Add [2] and [3] to eliminate the x term
0.12x + 0.20y = 176
+
-0.12x + 0.12y = 48
-----------------------------------------
0x + 0.32 y = 224
=> 0,32y = 224
Divide both sides by 0.32
==> 0.32y/0.32 = 224/0.32
==> y = 700
So 700 ml of Solution B was used
If we wanted to find volume of solution A used, subtract 400 from 700 to get 300 ml of A
Jessica is a software saleswoman. Her base salary is $1900, and she makes an additional $50 for every copy of History is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 28 copies of History is Fun.
Equation:
Total pay if Jessica sells 28 copies:
Answers
The equation which represents Jessica's income is 1900+50n.
Jessica's total income after selling 28 copies of History is Fun is $3300
Base salary of Jessica = $1900
The additional income per copy of History is Fun = $50
Let p represent her total pay (in dollars), and let n represent the number of copies of History is Fun she sells:
Formulating the equation we get the following:
Jessica's total pay = Base salary + Additional income per copy of History is Fun*Number of copies sold by Jessica
= 1900 + 50*n
Income, when she sells 28 copies of History, is Fun:
= 1900 + 50*28
= 1900 + 1400
= $3300
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I need help with Systems of 2 equations Word Problems. Could some one help?
Answers
Let x be the number of children and let y be the number of adults.
We know that the total number of attendants was 147, then:
[tex]x+y=147[/tex]We also know that each child ticket cost $4 and for each adult cost $12, and the total amount collected were $1156. Then we have:
[tex]4x+12y=1156[/tex]Hence we have the system:
[tex]\begin{gathered} x+y=147 \\ 4x+12y=1156 \end{gathered}[/tex]Now we have to solve the system. To do that we solve the first equation for y:
[tex]y=147-x[/tex]and we plug this value into the second equation and solve for x:
[tex]\begin{gathered} 4x+12(147-x)=1156 \\ 4x+1764-12x=1156 \\ -8x=1156-1764 \\ -8x=-608 \\ x=\frac{-608}{-8} \\ x=76 \end{gathered}[/tex]Now that we have the value we can find the value of y, then:
[tex]\begin{gathered} y=147-76 \\ y=71 \end{gathered}[/tex]Therefore there were 76 children and 71 adults.
If L, M and N are the midpoints of the sides of the triangle PQR, PR= 46, PQ = 40, and LN = 17, find each measure.; LM, MN, QR and the perimeter of LMN
Answers
LM = 23; MN = 20 ; QR = 34 ; Perimeter of LMN is 60
Here, we want to find the measures
From what we have, triangle LMN is formed by joining the midpoints of the triangle PQR
From the midpoint theorem, the sides of PQR are parallel and exactly half the measure of the sides they face
For example, LM is half PR
a) LM
[tex]LM\text{ = }\frac{1}{2}\times PR\text{ = }\frac{1}{2}\times46\text{ = 23}[/tex]b) MN
[tex]MN\text{ = }\frac{1}{2}\times PQ\text{ = }\frac{1}{2}\times\text{ 40 = 20}[/tex]c) QR
Here, QR will be twice the measure of LN
[tex]QR\text{ = 2}\times LN\text{ = 2}\times17\text{ = 34}[/tex]d) To find the perimeter of LMN, we have to add up the measure of the side lengths
We have this as;
[tex]\text{LMN = LM + LN + MN = 23 + 17 + 20 = 60}[/tex]If 8 - x = 17, then find the value
of 6x - 22
Answers
Answer: -25
Step-by-step explanation: 8 - x = 17 ~ x=-9 6*(-9)-22=-25
What is the value of x? S *+559 W 2x–71° X-30
Answers
As shown in the figure :
The sum of the central angles = 360
so,
[tex](x+55)+(2x-71)+(x-3)+55=360[/tex]Solve the equation for x :
[tex]\begin{gathered} x+55+2x-71+x-3+55=360 \\ 4x+36=360 \\ 4x=360-36 \\ 4x=324 \\ \\ x=\frac{324}{4}=81 \end{gathered}[/tex]So, the answer is : x = 81
Find a polynomial function of degree 4 with - 1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function in expanded form is f(x) = _
(Use 1 for the leading coefficient.)
Answers
Answer: [tex]f(x)=x^4 +3x^3 +3x^2 +x[/tex]
Step-by-step explanation:
[tex]f(x)=x(x+1)^3 \\\\=x(x^3 +3x^2 +3x+1)\\\\=x^4 +3x^3 +3x^2 +x[/tex]
PLEASE HELP ME ASAP
What is the slope of the line passing through (0, 5) an d(-12, 2) ?
Enter your answer in the box.
Answers
Answer:
Slope = 0.25
Step-by-step explanation:
m= -3 / -12 = -1 / -4 = 0.25
distance between x's = 12
distance between y's = 3
hope this helped thank you!
which equation would be used to find three consecutive even integers whose sum is 78
Answers
Let n be the smallest integer of the 3, then since all the numbers have to be even numbers, the other two numbers are of the form:
[tex]\begin{gathered} n+2, \\ n+4. \end{gathered}[/tex]Since the sum of the numbers has to be 78, we can set the following equation:
[tex]n+n+2+n+4=78.[/tex]Simplifying the above equation we get:
[tex]3n+6=78.[/tex]Answer:
[tex]3n+6=78.[/tex]
how many minutes does it take Julian to ride School
Answers
Given data:
The time taken by Amy is A=30 min.
The expression for the time taken by Julian is,
[tex]\begin{gathered} J=A+\frac{60}{100}A \\ =(1.6)A \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} J=1.6(30\text{ min)} \\ =48\text{ min} \end{gathered}[/tex]Thus, the time taken by Julian is 48 minutes.
what is the base and coefficient of the exponential function:
Answers
Given an exponential function
[tex]\begin{gathered} y=ab^x \\ \text{ wh}ere\text{ a and b are constants} \\ \text{then a is the coefficient} \\ \text{and b is the base} \end{gathered}[/tex]Therefore,
10 is the coefficient and 1/5 is the base
Whats the answer I DONT het how to do this At all
Answers
Given that the radius r of a circle is written as a function of the area A with the following equation:
[tex]r=\sqrt[]{\frac{A}{\pi}}[/tex]The domain of the above function is the area A of the circle.
This is because, in this context, the area is an independent and unique variable.
A is the input value.
1. You will receive $100 per year for 10 years. The discount rate is 10%. What is the
present value of this stream?
Answers
Answer:
100 ×10 =1000
Step-by-step explanation:
10% of 1000 is 100 that's the final answer if am wrong let me know
How many solutions can be found for the linear equation? 3(x+4)=3x+7
Answers
Answer:
there is no solution because there aren't any nubmer of X to get linear equation
3X-3X= 12-7
0=5
there aren't solutions so it will be 0
(One-Step Inequalities MC) Write the inequality for the statement: the difference between a number and four sevenths is no more than negative nine elevenths f minus 4 over 7 is less than or equal to 9 over 11 f minus 4 over 7 is less than negative 9 over 11 f plus 4 over 7 is less than or equal to negative 9 over 11 f minus 4 over 7 is less than or equal to negative 9 over 11
Answers
The inequality for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .
By definition, any monotonically growing function can be applied to both sides of an inequality without destroying the relationship between the two (provided that both expressions are in the domain of that function).
However, the inequality relation would be reversed if a monotonically declining function were applied to both sides of an inequality. Examples of using a monotonically declining function are the rules for the additive inverse and the multiplicative inverse for positive numbers.The inequality stays strict if the function is strictly monotonic and the inequality is strict (a b, a > b). The resulting inequality is non-strict if only one of these requirements is met. In fact, applying a strictly monotonically declining function is demonstrated by the criteria for both additive and multiplicative inverses.The inequality for the given statement is [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .
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Answer:
the answer is D.
Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
NEED FAST RESPONSE EQUATION AND SOLUTION
Answers
The equation is 6.75x = 5.875y
The price will be the same for 47 Go Golf games and 54 Golf Games
Go Golf charges for the ball and club rental = $2.50
Go Golf charges per game = $4.25
Total charges for Go Golf for one game = $6.75
Golf Games charges for the ball and club rental = $3.25
Golf Games charges for two games = $8.50
Total charges for Golf Game for two games = $11.75
Per game charges = $11.75/2 = $5.875
Let x be the number of games for Go Golf and y be the number of games for Golf Games
Formulating the equation we get:
6.75x = 5.875y
Converting into fractions we get:
675/100x = 5875/1000y
27/4x = 47/8y
After cross multiplication
x/y = 57/48
x = 57 and y = 48
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4. Which number produces anirrational answer when multipliedby 0.79?A.B. 0.383838...C. 0.12D.קשותU
Answers
Recall that the product between two rational numbers is always a rational number, and the product between an irrational number and a rational number different from zero is always an irrational number.
Also, recall that a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Now, notice that:
[tex]\begin{gathered} 0.79=\frac{79}{100}, \\ 0.383838\ldots=\frac{38}{99}, \\ 0.12=\frac{12}{100}. \end{gathered}[/tex]Therefore, 0.79, 0.383838..., 0.12 are rational numbers.
Now, recall that:
[tex]\sqrt[]{7}[/tex]is an irrational number.
Therefore, the product between 0.79 and √7 is an irrational number.
Answer: Option A.