Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.
Describe complimentary angles.A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way
Here,
Given : complementary angle one of the angle is 35°
=> x+ 35° = 90°
=> x = 55°
Let y be the supplement of angle x
=> x+ y = 180°
=>55° + y =180°
=>y =125°
Therefore , the solution of the given problem of angle comes out to be
x = 55° and y =125°.
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Say you take out a loan with a principal of $44,500. The interest rate is 13.11%, compounded monthly. If you make
consistent monthly payments and pay off the loan over the course of six and a half years, how much interest will you
have paid in total? Round dollar amounts to the nearest cent.
a. $21,849.92
b. $3,018.03
C. $20,003.60
d. $24,321.18
The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.
What is monthly compounding?Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.
Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.
Thus;
[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]
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A rectangle with an area of 5050 units^2
2
is the image of a rectangle that was dilated by a scale factor of \frac{1}{3}
3
1
. Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]
How can I inflate my model?Add the square of the scaling factor s to the area of the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of the figure after dilation Ad. a d = s2a p .
To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]
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Keshia goes to the post office to mail a package and a few letters. Stamps cost 49 cents each. It will cost $7.65 to mail the package. Keshila has 10.00. a. Write an inequality to represent this situation, where x is the number of stamps.
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
Define Inequality.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."
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What's the equation and solution?
Using the Algebraic tile method we get x=2 solution for equation model
What is Algebraic Tile method?The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.
In the question, we have 3 kinds of tile
X tilesunit positive tilesunit negative tilesEquation will be :
⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1
⇒ 3x - 2 = 4
⇒ 3x = 6
⇒ x = 2
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5) Is y = x^3 a function. Why or why not; please use complete sentences.
Yes, the expression; y = x³ is a function because it passes the vertical line test.
What is function?Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.
There are 4 types of functions:
Functions with arguments and return values Functions with arguments and without return valuesFunctions without arguments and with return valuesFunctions without arguments and without return valuesOn this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
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During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes. Based on this relative frequency, how many pars or better could he be expected to make on the remaining 150 holes? Round to the nearest whole number if necessary.
70 pars or better
60 pars or better
65 pars or better
53 pars or better
Dirk will make 70 pars or better.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.
Out of 90 holes, Dirk made par or better on 42 holes.
At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.
Then, Out of 150 holes, Dirk will make par or better on -
(42/90 x 150) holes
(42/90 x 150)
70
Therefore, Dirk will make 70 pars or better.
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50 POINTS Answer the following questions and draw a rough sketch of the function:
f(x)=-x^4+8x^3+8x^2-96x-144
What is the function’s general shape?
Does the function face up or down?
What is the function’s y-intercept?
If one of the factors is (−6), how would you show that on the graph?
The function's general shape is a downward-opening parabola.
The function faces down The function's y-intercept is -144x - 6 is a factorWhat is the function’s general shape?
From the question, we have the following parameters that can be used in our computation:
f(x)=-x^4+8x^3+8x^2-96x-144
Express properly
So, we have
f(x) = -x⁴ + 8x³ +8x² - 96x - 144
Next, we plot the graph (see attachment)
From the attached graph, we can see that the function opens down
This means that the general shape is a downward-opening parabola.
Does the function face up or down?The function faces down (as shown on the graph)
What is the function’s y-intercept?Here, we set x = 0
So, we have
f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144
Evaluate
f(0) = -144
So, the y-intercept is -144
How to show that one of the factors is (x - 6) on the graph?We start by setting the factor to 0
So, we have
x - 6 = 0
Solve for x
x = 6
From the graph;
When x = 6, y = 0
This means that x - 6 is a factor
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Suppose that the function h is defined, for all real numbers, as follows.
h(x) = (x+1)²
{
if x ≤-2
if-2
-x-2 ifx>2
h(-2) = 0
h(-1) = 0
h (3) = 0
Find h(-2), h(-1), and h (3).
0/0
믐
X
3
please help 15 points to whoever does
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
h(x) = (x+1)²
h(-2) = 1
h(-1) = 0
h(3) = 8
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
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graph f and h , write h in terms of f, describe the transformation from the graph of f to the graph of h .
the equation :
f(x) = 3x ; h(x) = 3x - 5
h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
What is the graph of the function?A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.
Here,
We can draw the graph as
h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)
h(x) = f(x) + 5
The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.
Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
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Mario had 8 1/5
yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
The closest to the number of yards of ribbon Mario had altogether will be ;
⇒ 11 yards
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Now,
Since, Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards
= 41/5 + 11/4
= (164 + 55) / 20
= 219 / 20 yards
= 10.95 yards
≈ 11 yards
Thus, Total ribbon for the project Mario have = 11 yards
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Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(5) when μ = 9
Answer: 0.155
Step-by-step explanation:
To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:
P(k) = (μ^k * e^(-μ)) / k!
Where:
P(k) is the probability of the event occurring k timesμ is the meane is the base of the natural logarithm ( approximately 2.71828)k! is the factorial of k (k factorial)Plugging in the given values, we get:
P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550
So the probability of the event occurring 5 times is approximately 15.5%.
Solve systems of equations by elimination -3x-3y=3 3x+6y=9
Answer: x = -5, y = 4
Step-by-step explanation:
Align the two equations according to their terms:
[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]
Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:
[tex]3y = 12\\y = 4[/tex]
Plug in y = 4 into the first equation:
[tex]-3x - 3(4) = 3\\[/tex]
Solve for x:
[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]
Check by plugging in both x and y:
[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]
So, x = -5 and y = 4
A woman has 31 coins in her pocket, all of which are dimes and quarters. If the total value of the coins is $ 5.20, how many dimes and how many quarters does she have?
Answer:
D+Q = 31
10D + 25Q = 595
10D + 10Q = 310
subtract to get
15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes
What is the coefficient in the expression 6 – 2 + 4n
Answer:
4
Step-by-step explanation:
The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.
Hope this helps! :)
How do I even do this?
Answer:
going to have to to get the house ready
Please help me solve
On solving the provided question, we can say that - the linear equation
y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y=mx+b
x=gallons of fuel
y=total weight of plane including fuel
m=slope=6.4
b=weight of plane, no fuel....a constant to be calc'd
[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]
82gallons fuel is 2424.80 lbs
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Y= 25x + 115
What is the rate of change and what does it represent?
Answer:
Step-by-step explanation:
y= 265
The rate of change of the equation is 25.
The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.
Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.
Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.
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b.) Suppose the Governor of Louisiana decided that all license plates must begin with the
letter A on each license plate. How many fewer license plates would
Louisiana be able to issue using the Governor's mandate for license plates?
Answer: atleast alot
Step-by-step explanation:
shia has 6 new boxes of crayons . each box has 8 crayons he also has 7 crayons from an old box how many crayons does he have
The answer is: 55 crayons.
Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!
AP TEST QUESTION 1
PLEASE HELP
ILL GIVE BRAINLIST ANSWER
IMAGE ABOVE
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x).
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
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Kemi is used division to write a fraction equivalent to 30/100. She tried to divide the numerator and denominator by 3. She got stuck what advice would u give her?
Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2
So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.
when reduced it would simplify back to 30/100.
You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.
Step-by-step explanation:
To purchase 12,100 worth of machinery for her business, Latoya made a down payment of 1800 and took a business loan for the rest. After 3 years of paying monthly payments of 313.36, she finally paid off the loan.
A, what was the total amount latoya ended up paying for the machinery. (including down payment and monthly payments)
B. How much interest did latoya pay on the loan
The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96
The amount of interest that Latoya paid was $ 980.96
How to find the total amount paid ?The total amount paid by Latoya for the machinery can be found as :
= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )
= 1, 800 + ( 313. 36 x 12 x 3 )
= $ 13, 080 .96
The total interest paid on the loan was :
= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment
= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800
= $ 980.96
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profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, what were profits last year.
The profits last year were $2041.66
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900
x=4900/2.4
x=2041.66
Hence, The profits last year were $2041.66
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PLSS GUYS HELP MEEEEEEEE PLS
The value of x is 10°.
What is a measure of an angle?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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The value of x is 10°.
What is a measure of an angle?Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
What is angle?An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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What is 15% of 12 meters?
Answer:
1.8 meters
Step-by-step explanation:
Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.
Answer: 1.8
Step-by-step explanation:
Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.
What is the value of sin(7pi/4)? See attached.
Answer:
-sqrt(2)/2 , the last option of your document.
Step-by-step explanation:
sin(7pi/4) = -sin(7pi/4 - pi)
= -sin(7pi/4 - 4pi/4)
= - sin(3pi/4)
sin(3pi/4) is a special angle , which is sqrt(2)/2
Hence, sin(7pi/4) = -sin(3pi/4)
= -sqrt(2)/2
Answer:
-sqrt(2)/2
Step-by-step explanation:
did the test
Anything would help please
When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)
what is triangle ?A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
area of the polygon ( triangle ) = 1/2 * b * h
= 1/2 * 4 * 4
= 8 units
so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)
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The graph below represents the linear equation y = 1/2x - 3.
A second linear equation is represented by the data in the table.
x | y
-1 | 1
0 | 0
2 | -2
3 | -3
What is the solution to the system of equations?
A) (-2, -4)
B) (1, -1)
C) (2, -2)
D) (4, -4)
Answer:
(2,-2)
Step-by-step explanation:
The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.
hope this helps :)
Answer:
C) (2, -2)--------------------------
From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:
y = - xThe first line is given y = 1/2x - 3, equate both to get:
- x = 1/2x - 3-2x = x - 6x + 2x = 63x = 6x = 2Then the value of y:
y = - x = - 2The solution is (2, - 2).
SELECT ALL of the numbers that are included within the range of the line segment.
ANSWERS ↓
-6
-4
-3
-2
0.5
1.5
3.5
Answer: -2, -3, and -4.
Step-by-step explanation:
The range is all the Y Values the graph uses, and the Y values range from -0.5 to -5.5, making every number in between those included.
Susan invested a total of $9000 in two accounts. One account pays 3% interest and the other account pays 6% interest. The total return from both accounts was $450.
The money invested in a account with 3% interest is $3000 and the money invested in a account with 6% interest is $6000.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, Susan invested a total of $9000 in two account.
One account pays 3% interest and the other account pays 6% interest.
Let the money invested in a account with 3% interest be x.
Then, the money invested in a account with 6% interest be 9000-x.
The total return from both accounts was $450.
Here, (x×3×1)/100 + ((9000-x)×6×1)/100 =450
3x+54000-6x=45000
54000-3x=45000
3x=9000
x=$3000
So, 9000-x=$6000
Therefore, the money invested in a account with 3% interest is $3000 and the money invested in a account with 6% interest is $6000.
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