Answer:
161 square inches.
Step-by-step explanation:
The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 7 inches, the area of the base is 49 square inches (7 inches x 7 inches).
To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.
To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
In this case, the base of the triangle is 7 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 7 inches x 8 inches = 28 square inches.
Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 28 square inches = 112 square inches.
To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 49 square inches + 112 square inches = 161 square inches. Therefore, the surface area of the pyramid is 161 square inches.
The spinner shown has eight congruent sections the spinner is spun 144 times what is a reasonable prediction for the spinner will land on an even number.
Prediction for the spinner will land on an even number is 54 times.
What do you mean by permutation and combination?
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
144 x 3/8 = 432/8 = 54
The answer would be 54 times.
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Name two sets of alternate interior angles.
Answer:
∠ a & ∠ d
∠ b & ∠
Answer:
∠ A and ∠ D
∠ B and ∠ E
Step-by-step explanation:
The equation x² - 4x + y2-2y = 16 describes a circle. What is the y-coordinate of
the center of the circle?
The y-coordinate of the center of the circle is 1.
What is a coordinate?
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates. A coordinate system is a framework for specifying how objects are situated in relation to one another within a specified space, such as a specific region of the earth's surface or the entire surface of the planet.
Solution Explained:
After completing the square for x and for y, you should get
(x+2)^2 + (y-1)^2 = 21
Center (x,y) = (-2,1)
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According to online realtor Zillow a 30 year $200,000, 4. 5%, fixed rate mortgage on your house will currently set your estimated monthly payments at about $1,020 per month. A 15-year fixed rate $200,000 mortgage would drop to 4. 0% with monthly payments of $1,480. Approximately how much would the 15-year fixed rate mortgage save you over the length of both loans?
The 15-year fixed rate mortgage save $ 100,800 more than in the case of the 30-year mortgage.
We must compute the total payments to be made in order to determine the amount saved by getting a 15-year mortgage rather than a 30-year mortgage.
Payments for a 30-year mortgage with a fixed rate of 4.5% are due every month in the amount of $1,020. The total payment is then determined as follows:
Total payment = 1020 * 12* 30 = 367,200
Difference according to lone = 367,200 - 200,000
difference = $167,200
Now, the monthly payments for the 15-year mortgage at a 4% rate will be $1,480.
Then total final payment = 1480*12*20 = $266,400
so in this case, the difference from The loan will be
266,400 - 200,000 = $66,400
Thus, we can draw the conclusion that, when comparing the two loans, the 15-year option will result in savings of $ 100,800 more than the 30-year mortgage.
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Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
−3.2 + b > 10.7
−3.2 + b < 10.7
b + 10.7 ≥ −3.2
b + 10.7 ≤ −3.2
The inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let the number be 'b'. Then the statement "the sum of a number and 10.7 is at most −3.2" is written in mathematical form. Then we have
b + 10.7 ≥ −3.2
Thus, the inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.
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i need help with this.. help please?? :,))
Answer:
C: adding on the right and subtracting on the left; n = 4S: dividing on the left and subtracting on the right; y = 2J: multiplying on the left and dividing on the right; b = 512Step-by-step explanation:
You want the solutions to three equations, and the error in the work shown.
Cullen: -6n +22 = -4n +14Seraphina: 8.4y -6.8 = -3.2y +16.4Jasper: 7/8b -32 = 3/4b +32CullenThe correct solution is ...
[tex]-6n+22=-4n+14\\\\22=2n+14\qquad\text{add $6n$}\\\\8=2n\qquad\text{subtract 14}\\\\\boxed{4=n}[/tex]
Cullen's error was adding 4n to one side, and subtracting 4n from the other side of the equation. (The same operation must be done to both sides.)
SeraphinaThe correct solution is ...
[tex]8.4y -6.8 = -3.2y +16.4\\\\11.6y-6.8=16.4\qquad\text{add $3.2y$}\\\\11.6y=23.2\qquad\text{add 6.8}\\\\\boxed{y=2}[/tex]
Seraphina's error was dividing one side of the equation by 11.6 and subtracting 11.6 from the other side. (The same operation must be done to both sides.)
JasperThe correct solution is ...
[tex]\dfrac{7}{8}b -32 = \dfrac{3}{4}b +32\\\\\dfrac{1}{8}b-32=32\qquad\text{subtract $\dfrac{3}{4}b$}\\\\\dfrac{1}{8}b=64\qquad\text{add 32}\\\\\boxed{b=512}\qquad\text{multiply by 8}[/tex]
Jasper's error was multiplying one side of the equation by 8 and dividing the other side by 8. (The same operation must be done to both sides.)
Aeris reads the temperature of a liquid in a lab experiment. The temperature of the liquid is 7.2ºF. After 5 hours, she reads the temperature of the liquid again. The temperature of the liquid is now −1.6°F.
Aeris plots the points on a number line to determine the temperature change between these two readings.
How much did the temperature decrease?
Enter your answer as a decimal in the box.
[]
Answer:
Step-by-step explanation:
5,6
Find the sum of 6 and 18.
12
× (6 +18) = X
?
Answer:
24
Step-by-step explanation:
6 + 8 =24. You can ignore the 1/2 because it is on both sides of the equation.
Answer:
it is 24 and 24x1/2 but you can count 1/2 as 2 which will get you to 48 division 12
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
Which of the following statements must be true about the polynomial function f(x)
For a polynomial function statements that need to be true are different end behavior for different degree and different sign of leading coefficient.
What is polynomial function?A function that can be expressed as a polynomial is referred to as a polynomial function.
A polynomial equation's definition can be used to derive the definition.
A polynomial is typically denoted by P (x).
The degree of the variable in P(x) is its maximum power.
The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large.
Whole real numbers make up a polynomial function's domain (R).
For a polynomial function following statements to be true:
Function that has different degrees have different end behaviors because due to different degrees the graph will be different, and their x-intercept will be different.Function that has leading coefficient of different sign have different end behavior because if we take even degree polynomial leading coefficient.To know more about polynomial follow link:
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the probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to . the odds that it will not rain tomorrow are to
The probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to . The odds that it will not rain tomorrow are to 0.8.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The probability that it will rain tomorrow is 0.2
i.e.
P(it will rain tomorrow )=0.2
Now probability that it won't rain tomorrow is,
P(it won't rain tomorrow )=1- P(it will rain tomorrow)=1-0.2=0.8
Thus
P(it won't rain tomorrow)=0.8.
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Me. Ramirez writes the equation shown. He asks four students to slice the equation for y 8x-4y=20
The slicing of the equation 8x - 4y = 20 for y is y = 2x - 5
How to slice the equation for yFrom the question, we have the following parameters that can be used in our computation:
8x-4y=20
Rewrite the above equation properly
So, we have the following representation
8x - 4y = 20
Divide through the equation by 4
So, we have the following representation
2x - y = 5
Make y the subject of the equation in the above equation
This gives
y = 2x - 5
Hence, the solution is y = 2x - 5
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Help……………………dldkdkldleld
Answer:
Angle DFC is complementary to angle BFC
Step-by-step explanation:
AD is a straight line passing line EB. DFE, EFA, AFB and BFD are right angles as the lines are perpendicular.
DFB is divided into 2 angles by the segment FC
therefore
DFC + BFC = 90 degrees
What is the value of g(5)-2g(1)
Answer:
3 grams
Step-by-step explanation:
g(5)-2g(1)
g × 5- 2g(1)
5g - 2g×1
5g - 2g
3g
Two Causal Relationships and One Correlation (Two Truths and a Lie)
Create three sets of two variables so that two sets describe causal relationships and one describes a correlation between the variables.
For example, one set of two variables that represent a causal relationship would be The number of people eating at a restaurant vs. The amount of food needed.
Please reply to the prompt and respond to two other students posts. You will earn 10 points for your initial response and 5 points for each reply. Students
may earn a max of 20 points.
How to respond to other posts:
• In one response, guess which set of variables represent the correlation.
. In the second response, describe how you could alter one of their causal relationships so it instead describes a borrelation.
However, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other. There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event.
Causal relationships between variables may consist of direct and indirect effects. Direct causal effects are effects that go directly from one variable to another. Indirect effects occur when the relationship between two variables is mediated by one or more variables.
Direct and indirect effects may make up causal connections between variables. Effects that flow directly from one variable to another are referred to as direct causal effects. When one or more factors mediate the link between two variables, indirect effects result.
What are examples of causal relationships?
Causal relationships: A causal generalization, e.g., that smoking causes lung cancer, is not about an particular smoker but states a special relationship exists between the property of smoking and the property of getting lung cancer.
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Pls help with thissss
2tan^2x+tanx=0
Find all angles that satisfy the equation below
The angles that satisfy the given trigonometric equation are 0°, 153.5°, 333.5°
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.
2tan^2∅ + tan∅ = 0
let k = tan∅
so that we have
2k^2 +k = 0
factorizing,
k( 2k + 1) = 0
Therefore,
k = 0, or 2k + 1 = 0
2k = -1
k = -1/2
so k = 0 or k = -1/2
recall that tan∅ = k
which means
tan∅ = 0 or tan∅ = - 1/2
∅ = arc(tan) 0 or arc(tan) -1/2
∅ = 0° 0r -25.6°
but tan ∅ = -1/2 at 90° to 180° and 270° to 360°
∅ = 0°, (180 - 25.55°), (360 - 25.55°)
∅ = 0°, 153.5°, 333.5°
In conclusion the angles that satisfy the equation are 0°, 153.5° and 333.5°
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you are to build a rectangular pen with three parallel partitions using 500 feet of fencing. what dimensions will maximize the total area of the pen?
The dimensions required are 125 feet and 50 feet.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.
The total length will be x and the height will be y.
Perimeter = 500 = 2x + 5y
Total Area = A = xy
Solve for y using the equation of perimeter:
5y = 500 - 2x
y = 100 - 2x/5
Put y in the equation of the Area
A = x(100 - 2x/5)
A = -2x²/5 +100x
To find the maximum area, find the derivative:
A' = -4x/5 + 100
To maximise the area, we equate A' to zero.
A' = 0
-4x/5 +100 = 0
∴ x = 125
A' is positive when x < 125 and A' is negative when x >125, therefore meaning that x=125 is a maximum. Since this value is a maximum, the area is maximized when the total length is 125ft.
Put x = 125 in equation of perimeter:
500 = 2(125) + 5y
500 = 250 + 5y
5y = 250
∴ y = 50 ft
Thus, the dimensions required are 125 feet and 50 feet.
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In the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 140 more people went to the pool than in the second week. In the fourth week, 315 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease of people who went to the pool is…
PLEASE I NEED A FAST ANSWER
TY‼️
The percent decrease of people who went to the pool is 25%.
Define percentage.Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.
Given
In first week = 1120
In second week
Subtracting,
1120 - 105
1015
In third week,
Sum
1015 + 140
1155
In fourth week
1155 - 315
840
The percentage of fewer persons that visited the pool during these four weeks,
1120 - 840/1120
280/1120
1/4
For percentage,
1/4 × 100%
25%
The percent decrease of people who went to the pool is 25%.
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Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chad strings the lights along the width of the ceiling, a distance of 48 feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used?
If necessary, round your answer to the nearest tenth.
feet
At the given point, Chad has used 176 feet of light
How to determine the number of feet of light?From the question, we have the following parameters that can be used in our computation:
Length = 55 feet
Width = 48 feet
We start by calculating the distance from the end of the width till the beginning of the length
This is represented by the following Pythagoras theorem
Distance = √(Length² + Width²)
So, we have
Distance = √(55² + 48²)
Evaluate
Distance = 73
The number of feet is then calculated as
Feet = Length + width + distance
So, we have
Feet = 55 + 48 + 73
Evaluate
Feet = 176
Hence, the total distance is 176 feet
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Which function represents the graph below?
The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
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The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
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Jim began a 255-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of
3 miles per hour and rides at 39 miles per hour, find the amount of time he spent on the bicycle.
The amount of time Jim spent on the bicycle is 6.5 hours.
What is distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
Total distance, d = 255 miles,
Total time, t = 7 hours,
The speed of walking, s = 3 miles / hour,
The speed of riding bicycle, S = 39 miles/hour,
Calculate the time spent on the bicycle as shown below,
Total time = Time on bicycle + Time walking
7 = Distance on bicycle/speed + Distance of walking / speed
7 = b / 39 + w / 3
Here w is the distance by walking and b is the distance covered by bicycle,
b + w = 255 (As given)
Solve both equations,
w = 1.5 miles and b = 255 - 1.5 = 253.5 miles
Calculate the time spent on a bicycle as shown below,
The time spent on the bicycle = b / 39
The time spent on the bicycle = 253.5 / 39 = 6.5 hours
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Find x, y and z for the diagram below.
X =
y =
Z=
88
2x+18
y+10
3x-7
The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
The value of x is 25.
The value of y is 78.
The value of z is 24.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure given we see that,
88 and y + 10 are corresponding angles.
88 = y + 10
y = 88 - 10
y = 78
Now,
3x - 7 and 2x + 18 are oposite angles.
3x - 7 = 2x + 18
3x - 2x = 18 + 7
x = 25
Now,
(y + 10) + (3x - 7) + z = 180
78 + 10 + 3 x 25 - 7 + z = 180
88 + 75 - 7 + z = 180
z = 180 - 156
z = 24
Thus,
The value of x is 25.
The value of y is 78.
The value of z is 24.
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Find compound interest on 15,625 at 4% for 3 years.
Help! With steps
Answer:
P=15,625
Rate=4%
Time=3 years
CI=P(1+R/100)^T
=15,625(1+4/100)^3
=15,625*1.124864
=17576 Ans
Step-by-step explanation:
hope it helps
Pls Help Got to do this right now!!!
Which expression is the additive inverse of - 13/6?
A) 13/6
B) 6/13
C) - 6/13
D) - 13/6
WILL MARK BRAINLIEST!!
. Is x + 2 a factor of the polynomial f(x)=2x^4-3x²-4x+1?
Of(2)=13, so (x + 2) is not a factor.
O f(-2)=29, so (x + 2) is not a factor.
O f(-2)=0,so (x + 2) is a factor.
Of(2)=0,so (x+2) is a factor.
(x + 2) is not a factor of the given polynomial f(x).
What is factor of polynomial?
A polynomial with coefficients in a specific field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Consider, the given polynomial
f(x)=2x^4-3x²-4x+1
We have to check that (x + 2) is a factor of polynomial or not.
Since, if (x - a) is a factor of polynomial then 'a' is a zero of polynomial.
Here if (x + 2) is a factor of f(x) then f(-2) = 0
Plug x = -2 in f(x).
⇒
f(-2) = 2(-2)^4 - 3(-2)^2 - 4(-2) + 1
= 32 - 12 + 8 + 1
= 20 + 9
f(-2) = 9
f(-2) ≠ 0
Hence, (x + 2) is not a factor of the given polynomial f(x).
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Silvia puts $1000 in an account. She puts 10% of the account each month for a year how much is in her account at the end of the year?
At the end of the year, there will be $2200.in her account
Describe account.A list of debit and credit entries for transactions involving a specific object (such as cash or notes payable), a certain person or business, or both. a financial period's transaction statement that displays the final balance
The most typical kinds of bank accounts are as follows: Checking accounts and Savings accounts
Silvia invests $1,000 in an account over the course of a year, contributing 10% per month.
Because there are 12 months in a year,
She puts 10% of the account each month for a year
that is 10 * 1000/100 = 100 each month she puts in her account.
so for 12months in a year 100*12 = $1200
$1200 in her account over the course of the year she has deposited
Thus, at the end of the year,
Silvia has $1000 + $1200 = $2200 in her account.
At the end of the year, there will be $2200.in her account.
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Which subset of real numbers does
belong to?
-17/20
The number -17/20 belongs to the set of real numbers.
What is the set of real numbers?
The set of real numbers is made by combining the set of rational numbers and the set of irrational numbers. Real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers.
All real numbers, including fractions and decimals, are part of the set of real numbers.
The set of real numbers includes all numbers that can be expressed on the number line, including positive and negative numbers, as well as all fractions and decimals.
This set is often denoted by the symbol "ℝ".
Hence, The number -17/20 belongs to the set of real numbers.
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Can 2/3 turn into an improper fraction
Answer:no
Step-by-step explanation:
Answer: no
Step-by-step explanation: cuz u need a number thats bigger such as the numerator is bigger than the denominator
5. Mila is preparing to travel from the United States to Belgium, a member of the European Union, and wants to exchange $80 USD to euros. She finds that the curren exchange rate is €0.85 EUR to $1 USD. If Mila exchanges $80 USD, how much mone will she receive in euros? (Example 4)
Mila will receive 68 EUROS of money after the exchange of 80 US dollar.
What is meant by USD?USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.
What is meant by EURO?Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.
According to the given data in the question,
1 USD =0.85 EURO
80 USD = 0.85*80 EURO
80 USD= 68 EURO
Hence 80USD will be converted to 68 EUROS
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Really need help on this I do not understand how to do anything
Answer:
y = 6x + 12
Step-by-step explanation:
(2, $24)
(4, $36)
(6, $48)
Find slope (y2-y1) / (x2-x1)
m = ($36 - $24) / (4 - 2)
m = 12 / 2
m = 6
Put into formula y = mx + b
y = 6x + b
Substitute values to find b (the y offset)
$24 = 6(2) + b
$24 = 12 + b
b = $12
y = 6x+12