The required measure of the smallest angle in the triangle is 37°.
What is Right angled triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
According to question:We know that one angle in right angled triangle is 90 degree and sum of other two angle is 90 degree.
So, acute angles are (2x -3) and (3x-7).
Then
(2x -3) + (3x-7) = 90
5x - 10 = 90
5x = 100
x = 20
Smallest angle = 2x - 3
= 2(20) - 3
= 40 - 3
= 37°
Thus, required Smallest angle is 37°
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Solve the problem by entering and solving an equation.
A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 14 inches. What is the width of the frame?
The solution is Blank (blank + w)= blank The width of the frame is blank inches.
The width of the given rectangular frame of perimeter of 52 inches is; 12 inches.
How to find the perimeter of a rectangle?The formula for perimeter of rectangle is;
Perimeter = 2(Length + width)
Now, we have the parameters as;
Perimeter = 52 inches
Length = 14 inches
Thus, plugging in the relevant values into the perimeter equation gives;
52 = 2(14 + width)
52/2 = 14 + width
14 + width = 26
Width = 26 - 14 = 12 inches
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz. of glue and 7.6 oz. of glitter to make 4 bottles.
The correct option is D.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
Given in the table,
Bottles Glue Glitter
1 3.8 1.9
Therefore
1 bottle = 3.8 oz. of glue + 1.9 oz. of glitter
Now,
Multiply 4 on both sides.
4 bottle = 4 x (3.8 oz. of glue + 1.9 oz. of glitter)
4 bottle = 15.2 oz. of glue + 7.6 oz. of glitter
Hence, 15.2 oz. of glue and 7.6 oz. of glitter is needed to make 4 bottles.
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Select True or False for each statement. True False The equation y=3x−5 represents a function. True – The equation , y equals 3 x minus 5, represents a function. False – The equation , y equals 3 x minus 5, represents a function. A function can only be represented by a straight line on the coordinate plane. True – A function can only be represented by a straight line on the coordinate plane. False – A function can only be represented by a straight line on the coordinate plane.
The statement "The equation y = 3x - 5 represents a function." is; TRUE
The statement "A function can only be represented by a straight line on the coordinate plane." is; FALSE
How to represent Linear Functions?A linear function is one that is formed when a variable y varies directly with a variable x. That is, when y increases, x also increases and the opposite is also true.
The equation y = 3x - 5 represents a function. This statement is said to be true because every value of x gives a different value of y and as such we can say it maps different elements to different images.
A function can only be represented by a straight line on the coordinate plane. This statement is false because a function can also be represented by a circle, ellipse, parabola, etc.
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Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
13
12
Step-by-step explanation:
that is really simple, because the additional half-circle compensates for the missing half-circle on the other side.
so, the area is plain and simple the area of the rectangle, which is
13×12 = 156 = 156.0
Convert 9 days into weeks. Round your answer to the nearest hundredth.
-2(c+2.5)-5(1.2c+4) simplify this expression
Answer: - 8c - 25
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
Match the below functions to their graphs on the right:
These are functions that almost have to be memorized but can be understood through Desmos for example:
a: W
b: Z
c: X
d: Y
e: V
Zahra invested $8,800 in an account paying an interest rate of 8 5/8% compounded annually. Christopher invested $8,800 in an account paying an interest rate of 8 1/4% compounded daily. After 11 years, how much more money would Zahra have in her account than Christopher, to the nearest dollar?
After 11 years, the amount (future value) in Zahra's account will be $58 more than the amount in Christopher's.
How the future value is determined?The future value can be determined by using the FV table or formula.
We can also ascertain the future value using an online finance calculator as follows:
Zahra's Investment:N (# of periods) = 11 years
I/Y (Interest per year) = 8.625%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,863.03
Total Interest = $13,063.03
Christopher's Investment:N (# of periods) = 4015 days (11 years x 365)
I/Y (Interest per year) = 8.25%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,805.22
Total Interest = $13,005.22
Future Values:Zahra's = $21,863.03
Christopher's = $21,805.22
Difference = $57.81 ($21,863.03 - $21,805.22)
Thus, with a slightly higher interest rate, Zahra's account will generate $58 more in future value than Christopher's investment.
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The ratio of the perimeter of a square piece of paper to the perimeter of a rectangular piece of paper is 2 : 5. Each side of the square piece of paper is 10cm. Find A. The perimeter of the square piece of paper B. The perimeter of the rectangular piece of paper C. The length of the rectangular piece of paper if its width is 15cm ( Please answer all parts!)
The perimeter of the square piece of paper is 40 cm .The perimeter of the rectangular piece of paper is 50 cm and the length of the rectangular piece of paper is 15 cm.
A. The perimeter of the square piece of paper is 40 cm.
This is calculated by multiplying the length of each side of the square by 4.
Length of each side = 10cm
Perimeter of square = 4 x 10 cm = 40 cm
B. The perimeter of the rectangular piece of paper is 50 cm.
This is calculated by multiplying the length and width of the rectangle by 2.
Length = 15 cm
Width = 15 cm
Perimeter of rectangle = 2 x (15 + 15) cm = 2 x 30 cm = 50 cm
C. The length of the rectangular piece of paper is 15 cm.
This is given in the question.
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the preference card calls for 0.25% marcaine and 1% lidocaine to be equally concentrated. how much marcaine will you need to draw up to equal the 1% l
4.0 mL of marcaine will be needed to draw up to equal the 1%.
Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.
To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:
(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)
In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:
1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)
To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:
(Volume of Lidocaine) / (Volume of Marcaine) = 4
Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.
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What term and 12x^2 have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial
If the GCF of a term and 12x²y is 4xy , then (a) The term is 8xy , The expression is 4xy(2 + 3x) .
The Greatest Common Factor of the two terms is 4xy ,
where , the first term is 12x²y , we have to find the second term ,
Consider Option(a) : where the second term is 8xy ,
So , GCF of 8xy and 12x²y is
= 2(4xy) and 3x(4xy)
= 4xy(2 + 3x ) ....taking 4xy common from both the terms ,
Therefore , Yes , the second term is 8xy and the expression is 4xy(2+3x) .
The given question is incomplete , the complete question is
What term and 12x²y have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial , choose the correct answer below :
(a) The term is 8xy , The expression is 4xy(2 + 3x)
(b) The term is 16xy , The expression is 4xy(4xy + 3x)
(c) The term is 3x , The expression is 12x²y(3x + 4xy)
(d) The term is 4x²y , the expression is 4xy(1 + 3x) .
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The cost of a bicycle wheel was $62 last week. This week, the cost rose to $79 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
the percentage increase is 27.4%
Step-by-step explanation:
To find the percentage increase, we can use the formula:
(New cost - Old cost) / Old cost x 100% = Percentage increase
(79 - 62) / 62 x 100% = 27.41%
The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%
Difference of $62 and $79 is 24.1%
62 - 79/((62 + 79)/2) = 17/70.5 =
0.24113475177305 x 100 = 24.113475177305%
Question 3 (2 points)
What translation takes the graph of f(x) = 4x - 3 to the graph of g(x) = 4x - 6 ?
Translation of 3 units down
Translation of 6 units left
Translation of 6 units down
Translation of 3 units right
Answer: The graph of g(x) = 4x - 6 is a translation of the graph of f(x) = 4x - 3.
A translation of a function results in a shift of the graph of the function, either horizontally (left or right) or vertically (up or down).
When the graph of a function is shifted down, the y-coordinates of all the points on the graph decrease. When it's shifted to the left, the x-coordinates of all the points on the graph decrease.
In this case, the graph of g(x) = 4x - 6 is a vertical translation of 3 units down from the graph of f(x) = 4x - 3.
The y-coordinates of all the points on the graph of g(x) = 4x - 6 are 3 units less than the y-coordinates of the corresponding points on the graph of f(x) = 4x - 3.
Therefore, the correct answer is:
Translation of 3 units down.
Step-by-step explanation:
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
OA.
OB.
OC.
OD.
OE.
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
-
를
1/02/m
1
N/W
base area = B
h
base area = B
The ratio of the volume of the cone to the volume of a prism is equal to one.
What is volume?Three-dimensional space is quantified by volume. It is frequently measured quantitatively with SI-derived units (such the cubic metre and litre) or with a variety of imperial or US-standard units (such as the gallon, quart, cubic inch). Volume and height are related in how they are defined (cubed). The volume of a container is typically thought of as its capacity, or the amount of fluid (gas or liquid) that it could hold, as opposed to the amount of space the container occupies. Utilizing naturally occurring containers of a comparable shape and subsequently, standardized containers, volume is measured. Arithmetic formulas make it simple to determine the volume of some basic three-dimensional shapes.
We know that
The volume of the cone = area of the base. height/3
The volume of Prism = area of the base. height
Since the area of the base and height are the same hence the volume will also be . so the ratio will be 1.
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A coffee shop sells bags of coffee for
$9.90 per kilogram. Each bag holds 0.5 kilogram of coffee.
How many bags of coffee do they sell if they earn $702.90?
Explain your answer.
Answer:
142 bags
Step-by-step explanation:
0.5KG is half of a KG, so we can start by finding half of $9.90
$9.90/2 being $4.95
So each bag is $4.95
The total is $702.90
Dividing $702.90/$4.95 will equal the number of bags
702.9/4.95=142 bags
5. Suppose the following table shows the number of labor hours needed to produce airplanes and automobiles in the United States and South Korea, but one of the numbers is unknown.
Number of Hours to Produce One Airplane
South Korea 2000 United States 1000
Number of Hours to Produce One Auto
?
10
a. Without knowing the number of labor hours required to produce an auto in South Korea, you can’t figure out which country has the comparative advantage in which good. Can you give an example of a number for the empty cell of the table that would give the United States the comparative advantage in the production of airplanes? What about South Korea?
b. What exact number would you have to place in the empty cell of the table for it to be impossible that trade between the United States and South Korea could benefit both
The number for an empty cell would be 20 so any number below this benefit South Korea and above this benefit the United States. This also makes it impossible for trade between these two countries.
If a country can manufacture a significant number of goods with the same resources as another country, it has an absolute advantage. If a country can manufacture a certain commodity more cheaply and with higher quality than another country, it has a comparative advantage.
In the given scenario, 1000÷10=100 autos are sacrificed by the United States to manufacture one airplane which is the opportunity cost. In comparison to the United States, South Korea requires twice (2000÷1000) as long to construct an airplane.
a) The number of hours for South Korea to produce one auto would be 2×10=20. Because of this, South Korea would benefit from any number below 20, while the US would benefit from any number above 20.
b) The empty cell value would be 20 for South Korea to have the same opportunity cost as the United States. So mutually beneficial trade cannot exist without comparative advantage.
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Solve for EG. Enter your answer in the box.
Answer:
EG = 44
Step-by-step explanation:
EG, the whole thing, is 10x - 16. It says that at the top of the image. But also, under the segment, we can put together two small pieces, EF and FG. So, the whole thing could also be 4x + 20.
The two expressions both describe EG. They are equal to each other. Write an equation.
10x - 16 = 4x + 20
subtract 4x
6x - 16 = 20
add 16
6x = 36
divide by 6
x = 6
They are asking for EG. Use either expression.
EG = 4x + 20
= 4(6) + 20
= 24 + 20
= 44
or,
EG = 10x - 16
= 10(6) - 16
= 60 - 16
= 44
Actually, its a neat check to do both ways bc it should come out the same.
EG = 44
Complete the statement about the model.
The model shows that there are 8 groups of
in 3.
According to the diagram, there are eight fractions of 3/8 in three.
What is a fraction?A fraction is a ratio of two numbers where the numerator and denominator are both integers that can be negative or positive. The numerator can't be zero. Proper fractions and improper fractions are the two types of fractions.A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction's numerator will be less than the denominator.We are shown a diagram of three equal parts divided into eight equal parts.
Divide 3 by 8 to get the value of the equal part.
As a result, the value of each can be given as 3/8.
Therefore There are 8 groups of 3/8 in 3 as per the given diagram.
The diagram is attached below:
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A certain space shuttle travels at a speed of 3. 6 x
104 miles per hour. How many hours would it take
this space shuttle to travel 7. 2 x 108 miles?
It would take 2 hours for this space shuttle to travel 7. 2 x 108 miles
As per the given data, a certain space shuttle travels at a speed of 3. 6 x
104 miles per hour.
Here we have to determine that how many hours would it take this space shuttle to travel 7. 2 x 108 miles.
The relation between the speed and the distance is:
Speed = Distance × Time
Speed = 3. 6 x 104 miles per hour
Time = 1 hour
3. 6 x 104 = Distance × 1
Distance = 374.4 miles
The distance to be covered 7. 2 x 108 miles
= 777.6 miles
Hours taken to travel 7. 2 x 108 miles.
Time = [tex]\frac{777.6 }{374.4}[/tex]
≅ 2 hours.
Therefore the time taken to travel 7. 2 x 108 miles is 2 hours.
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A swim club bought a box of c swim caps to split evenly among its 20 members. Write an expression that shows how many swim caps each swimmer will get.
Answer:
20/C=X
Step-by-step explanation:
C= swim caps
X=How many swim caps each swimmer gets
what is x+5=8 step by step
Answer:
x = 3
Step-by-step explanation:
x+5=8
x+5-5=8-5
X=3
Answer:
x = 3
Step-by-step explanation:
basically 2 ways
1st: Transposing
1) x + 5 = 8
2) transpose or transfer +5 to the other side
NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)
3) x = 8 - 5
x = 3
2nd: Property of Equality (whatever u do one one side, you do the same to the other)
1) x + 5 = 8
2) x + 5 - 5 = 8 - 5
x = 3
the main focus is to isolate x, or to make it be alone in one side of the equation
WILL GIVE BRAINLIEST
Find the average rate of change for the given function from x = −1 to x = 2
The average rate of change for the given function from x = −1 to x = 2 is -4/3
How to find the average rate of change for the given function from x = −1 to x = 2?The average rate of change of a function over an interval is a measure of how much the output of the function (y-value) changes as the input (x-value) changes over that interval. This is also the slope of the function or line.
average rate of change = (y2-y1)/(x2-x1)
From the graph, x1 = -1, y1 = 4 and x2 = 2, y2 = 0
average rate of change = (0-4)/(2-(-1)) = -4/3
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Write an equation for the secant line of the function Y =X^4 on the interval [1,2]
The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).
How do you find the equation of a secant line over an interval?The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).
Slope is the term used to describe when one end or side of a surface is higher than the other. A Secant line is a straight line that connects two points on a function. formula for secant line slope.
A secant line's slope through two points is equal to y 2 y 1 x 2 x 1. On the secant line, locate two spots.Discover the line's slope between the two spots.To get the line's equation, enter one of your points and your slope into the point slope form of your line.
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a certain phone company charges $4.50 for the first five minutes of an international phone call. additional time is charged at $.50 per minute. how much would a customer be charged for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day?
A customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.
Charge for first 5 charged = $ 4.50
Charge for additional time = $ 0.50 per minute
Starting time = 9:35 p.m.
End time = 11:15 p.m.
Total minutes = 100 minutes
Total charge = 4.50 + (95 x 0.50)
= 4.50 + 47.50
= 52.00
Hence, a customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.
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Prove the Pythagorean Theorem with Similar Triangles using a two-column proof.
Answer:
u
Step-by-step explanation
Find the volume of the solid obtained by rotating the region bounded by y=x2 , y=0, and x=1, about the y-axis.
The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.
We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.
We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.
y = x^2
Taking square root on both side, we get
x = √y
We can write it as
x = y^{1/2}
The volume integral formula is
V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]
The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.
Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.
Thus, a = 0 and b = 1 are the values.
Now, we may use definite integral to express the volume.
V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]
Now simplify
V = [tex]\pi\int_{0}^{1}ydx[/tex]
Now integrating
V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]
V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]
V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]
V = π/2
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Laura needs 139 programs for the school play on Thursday. How many boxes of programs will she need, given that each box contains 37 programs?
A triangle has a perimeter of 9x + 6. The first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. What is the length of the third side of the triangle?
x + 13
x − 1
8x − 7
17x − 1
The length of the third side of the triangle is x + 13.
What is the length of the third side of the triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The perimeter of a triangle is the sum of the length of all three sides of the triangle.
Given the data in the question;
Perimeter P = 9x + 6Side A = 5xSide B = 3x - 7Side C = ?To find side C, equate the sum of all three sides of the triangle to the perimeter and simplify.
Side A + Side B + Side C = P
5x + ( 3x - 7 ) + Side C = 9x + 6
5x + 3x - 7 + Side C = 9x + 6
8x - 7 + Side C = 9x + 6
Side C = 9x + 6 - ( 8x - 7 )
Side C = 9x + 6 - 8x + 7
Side C = x + 13
Therefore, side C is x + 13.
Option A) x + 13 is the correct answer.
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Answer:
x + 13
Step-by-step explanation:
i took the test xx
students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a
Students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a hypothesis.
A hypothesis is a proposed explanation or prediction about a phenomenon, based on limited information or data. It is a tentative statement about the relationship between variables that can be tested through further investigation or experimentation.
In scientific research, a hypothesis provides a framework for designing and conducting experiments to gather evidence to support or reject the hypothesis. It acts as a starting point for scientific inquiry and helps guide the research process.
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Which is the approximate percentage of total pay that fringe benefits make up?
O
O
4%
10%
15%
30%
O
The approximate percentage of total pay that fringe benefits make up is 10%
The term called percentage in math is defined as a number or ratio that can be expressed as a fraction of 100
Here we have to find the approximate percentage of total pay that fringe benefits make up.
As the total compensation offered to the workers or employees by employers in different countries can usually be bifurcated into two broad components.
Here we have to know that the first one is based on wages & salaries components and the second one is the fringe benefits component.
Here this one includes the benefits components usually consist of supplementary benefits such as gratuity, pension contribution, transportation service, accommodation facility, etc.
Here as per the report published by the Bureau of Labor Statistics, U.S. Department of Labor in 2020 said that the approximate of the total pay that the fringe benefits make up usually range from 26.1% - 37.3%.
Based on that the percentage of fringe benefits could vary from the type of industry such as the goods-producing industry or service-providing industry.
So, the increased percentage is calculated as
=> 37.3 - 26.1
=> 11.2
Therefore, the correct option is (b).
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