The simplified expression is 3a + 5ay - 3y -52 .
(a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
In the question ,
the algebraic expression is given as 3a+2y+5ay-2y-52-3y
to simplify it , we first group them in like terms
the expression becomes .
= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y
= 3a + 5ay + 2y - 2y - 3y - 52
= 3a + 5ay - 3y -52
Part(a)
the number of terms in the simplified expression is 4 ,
Part(b)
as we can see that the terms -3y and -52 are negative
So , there are 2 negative terms in the expression.
Therefore , (a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
The given question is incomplete , the complete question is
Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
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Determine the intercepts of the line.
Do not round your answers.
y=-2x - 21
x-intercept:
y-intercept:
The x intercept of y = -2x - 21 is [tex]\frac{-21}{2}[/tex]
The y intercept of y = -2x - 21 is -21
What is x - intercept and y - intercept of a line?
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given equation of line is
y = -2x - 21
For x intercept, we have to put y = 0
[tex]-2x - 21 = 0\\2x = -21\\x = \frac{-21}{2}[/tex]
So the x intercept is [tex]\frac{-21}{2}[/tex]
For y intercept, we put x = 0
[tex]y = -2\times 0 -21\\y = -21[/tex]
The y intercept is -21
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The volume of cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(2)=8
The best interpretation of the function v(2) = 8 is that the volume of a cube with side length of 2 units is 8 cubic units
What are function notations?Function notations are the representation of a function using expressions such as g(x), f(x), etc
How to determine the best interpretation of the function notation?From the question, we have the following function notation that can be used in our computation:
v(2) = 8
From the question, we have the following representation
v(s)
This means that the volume of a cube of side length s is v(s)
When the above function is compared to v(2) = 8, we have the following comparison
s = 2 and v(s) = 8
This means that a cube of side length 2 has a volume of 8
The above represents the best interpretation of v(2) = 8
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What is the slope of a line that is perpendicular to y = 6/7x + 2 and passes through point (−2, 3)?
The slope of the line that is perpendicular to y is m=6/7.
What do you mean by slope?
A number used to define a line's direction and steepness in mathematics is called the slope or gradient of the line.
The slope is denoted by m,
m = slope
According to the data in the given question:
We have to determine the slope of line that is perpendicular to y,
y=6/7x+2
For the slope, we need follow this equation, where m is slope,
y=mx+b............(1)
In the given question,
m=6/7
Therefore, the slope of the line is m=6/7.
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A) The data modelling is an exponential function.
B) The explicit funciton that will be used to represent the data is;
f(n) = 2(2)^(n - 1)
C) The average rate of change here is; 7
How to model a function?A) We are given the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16)
From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.
Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.
B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:
f(n) = ar^(n - 1)
Since first term ; a = 2
and common ratio r = 2, then we can say that;
f(n) = 2(2)^(n - 1)
C) The formula for average rate of change here is;
dy/dx = (y₂ - y₁)/(x₂ - x₁)
The coordinates of the 2nd and 4th day are;
(2, 4) and (4, 16)
Thus;
dy/dx = (16 - 4)/(4 - 2)
dy/dx = 14/2 = 7
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It is expected that 750 people will attend
the concert. In fact, 600 people attended.
600 is what percent of the expected
number?
600 is the 80% of the the expected number
Number of people that expected to attend the concert = 750 people
Number of people that attended the concert = 600 people
600 is what percent of the expected number = ( Number of people that attended the concert ÷ Number of people that expected to attend the concert ) × 100
Substitute the values in the equation
600 is what percent of the expected number = (600 / 750) × 100
Divide the terms in bracket first
= 0.8 × 100
Multiply the given terms
= 80%
Hence, 600 is the 80% of the the expected number
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Two photos are similar the ratio of the corresponding side length is 3:4 what is the ratio of their areas
The ratio of the areas of these two photos is equal to 9:16.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities.
This ultimately implies that, a ratio is generally expressed as a quotient of two numerical quantities or variables.
Generally speaking, the corresponding ratio of the areas of two geometric figures (shapes) is equal to the square of the ratio of their corresponding side length:
Area of photos = (a:b)²
Substituting the given parameters into the formula, we have;
Area of photos = (3:4)²
Area of photos = 9:16
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NEED HELP ASAP
What is the value of y in the solution to this system of equations 6y+x= -59 x= -2y+9?
Answer:
y = - 17
Step-by-step explanation:
6y + x = - 59 → (1)
x = - 2y + 9 → (2)
substitute x = - 2y + 9 into (1)
6y - 2y + 9 = - 59
4y + 9 = - 59 ( subtract 9 from both sides )
4y = - 68 ( divide both sides by 4 )
y = - 17
the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.
Answer:
L = 6 feet ; W = 4 feet
Step-by-step explanation:
l = 2 + w
perimeter/2 = 8
l + w > 8
2 + w + w > 8
2 + 2w > 8
2w > 8-2
2w > 6
2/2 w > 6/2
w > 3
smallest integer > 3 = 4
W= 4
L = 4 + 2 = 6
Rodrigo needs a total of 3 pounds of vegetables for a stew.
He already has 3/8 pound of onions and 1/3 pound of tomatoes.
How many more pounds of vegetables does he need to buy?
Using mathematical operations of addition and subtraction, Rodrigo needs to buy additional 2⁷/₂₄ pounds of vegetables.
What are mathematical operations?The basic mathematical operations are addition, subtraction, division, and multiplication.
These mathematical operations can be used to determine the results of mathematical expressions.
The total pounds of vegetables required for a stew = 3 pounds
Available pounds of vegetables:
Onions = 3/8 pounds
Tomatoes = 1/3 pounds
The total available pounds = 17/24 pounds
Additional pounds required = 3 - 17/24 pounds
= 2⁷/₂₄ pounds
Thus, based on addition and subtraction, Rodrigo needs additional 2⁷/₂₄ pounds of vegetables.
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If a = 4, then a³ + a=
I know the answer but can someone explain step by step
Answer:
D) 16
Step-by-step explanation:
A=4
[tex]a^3[/tex]/a=?
[tex](4^3)[/tex]/(4)=?
64/4=16
What is the equation in slope-intercept form of the line that passes through the point (2, -1) and is perpendicular to the line represented by y=x+4?
y=32-4
y=3x+4
y=-32-2
y=-3x+2
The slope-intercept form is
y = - x + 1
Given points are (2, - 1)
and y = x + 4
The product of slopes of perpendicular lines is - 1
so , m = - 1/1 = -1
y = mx + b-1 = (-1) (2) + b -1 = -2 + b-1 + 2 = b b = 1∴ y = -1 (x) + b
y = - x + 1
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It takes an older computer 3 times as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 15 minutes to send out the email. How long will it take the older computer to send out the email on its own?
60 minutes will be taken by the older computer to send out the email on its own.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
one computer takes x minutes and the other takes 3x minutes
in 1 minute, they send (1/x) and (1/3x) of the total message
together, (15/x)+(15/3x)=1, the full message
multiply by 3x to clear fractions
45+15=3x
60=3x
Divide both sides by 3
20=x
So for older computer 60 minutes it take to send out the email on its own.
Hence, 60 minutes will be taken by the older computer to send out the email on its own.
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REMEMBER 4. What is the difference in length? Carrot 14 cm Show the difference in length two ways. Write an equation for each. The difference in length is Pea pod 5 cm cm.
The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to determine the difference in lengths
The length of the carrot = 14 cm
The length of the pea pod = 5 cm
The difference in lengths = maximum length - minimum length
The difference in lengths = 14 cm - 5 cm
Apply the subtraction operation, and we get
The difference in lengths = 9 cm
We conclude that the length of the carrot is 9 cm longer than the pea pod.
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if q is 3x+ 6 and AC is 8x+8 what is the length of AC? Round your answer to the nearest hundredth
Answer:
AC = 24Step-by-step explanation:
AC is the diagonal of the parallelogram ADCB.
q is half of AC, therefore:
AC = 2qSubstitute values and solve for x:
8x + 8 = 2(3x + 6)8x + 8 = 6x + 128x - 6x = 12 - 82x = 4x = 2Find the length of AC:
AC = 8*2 + 8 = 16 + 8 = 244.5,3,1.5,0 fin the difference in the following sequence
-1.5 is the difference in the sequence
How determine the difference in a sequence?
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.
The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3
Given: the sequence 4.5,3,1.5,0
The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5
Note: You can pick any two consecutive terms to get the difference
Therefore, the difference in the sequence is -1.5
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81 to the 5th power = 3x
x=?
The value of x according to the given equation as in the task content is; 3¹⁹.
What is the value of x according to the given expression?It follows from the task content that the value of x is to be determined from the equation given in the task content.
Therefore, since the equation given in the task content is;
(81)⁵ = 3x
(3⁴)⁵ = 3x
3²⁰ = 3x
Therefore, the value of x can be evaluated as;
x = 3²⁰/3
x = 3¹⁹.
Ultimately, the value of x from the given equation is; 3¹⁹.
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Please help!
Find the amount of money( future value) in an account where 8,800 is deposited ( present value) at an interest rate 6.5% per year compounded continuously and the money is left in the account for 7 years.
The final amount is $ ?
Round your answer to 2 decimal places.
By using the formula for amount of money in a compound interest, it can be calculated that
Amount received after 7 years is $13675.08
What is a compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then
amount = [tex]p(1+\frac{r}{100})^n[/tex]
Difference between amount and principal gives the compound interest.
Principal = $8800
Rate = 6.5 %
Time = 7 years
Amount received = [tex]8800(1 + \frac{6.5}{100})^7[/tex]
$13675.08
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PLS HELP QUICK!! IL MARK YOU BRAINLIEST
A cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table. Sophie chooses a container at random. What is the probability that she chooses low-fat yogurt?
Answer:
Step-by-step explanation 2/3 is the answer :
The required probability, that she chooses low-fat yogurt is 2/3.
Given that, a cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
From the given,
Sample space = 24
Low Fat =16
Non-fat = 8
The probability that she chooses low-fat yogurt
= 16/24
= 2/3
Thus, the required probability, that she chooses low-fat yogurt is 2/3.
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What is the simplest fraction equal to 9%?
Suppose that y varies directly with x, and y=4 when x = 10.
(a) Write a direct variation equation that relates and y Equation: y =
Answer:
y = 0.4x
Step-by-step explanation:
given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 4 when x = 10 , then
4 = 10k ( divide both sides by 10 )
[tex]\frac{4}{10}[/tex] = k , that is
k = 0.4
y = 0.4x ← equation of variation
4 + x = 13 can be solved using the Subtraction Property of Equality. true or false
Answer: True
PLEASE GIVE ME BRAINLIEST THANK YOU VERY MUCH
True, the Subtraction Property of Equality can be used to solve it.
The equality subtraction property refers to balancing an equation by performing the same mathematical operation on both sides.
Let's work through your equation step by step.
4+x=13
Step 1: Take 4 off both sides.
4+x−4=13-4
x=9
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ANSWER PLEASE!
Armando lost 975 coins playing his
favorite video game. He lost the same number of coins in each of the 15 levels he played. What was the change in Armando's coins at the end of each level of the game?
Answer: 81.25
Step-by-step explanation:
Answer:
Armando lost 65 coins each level.
Step-by-step explanation:
Given information,
→ Armando lost 975 coins playing his favorite video game.
→ He lost the same number of coins in each of the 15 levels he played.
Forming the equation,
→ 15x = 975
Now required value of x will be,
→ 15x = 975
→ x = 975/15
→ [ x = 65 ]
Hence, he lost 65 coins each level.
Write an expression, in terms of h, for the perimeter of this triangle.
Simplify your answer fully.
7
14-6h
3h+3
Answer:
P = 24 - 3h-----------------------------------
It is assumed the sides of the triangle are7, 14 - 6h and 3h + 3Perimeter is the sum of three sidesP = a + b + cP = 7 + 14 - 6h + 3h + 3 = (7 + 14 + 3) + (3h - 6h) = 24 - 3hAnswer:
Perimeter = -3h + 24
Step-by-step explanation:
Forming the expression,
→ 7 + (14 - 6h) + (3h + 3)
Let's simplify the expression,
→ 7 + (14 - 6h) + (3h + 3)
→ 7 + 14 - 6h + 3h + 3
→ (-6h + 3h) + (7 + 14 + 3)
→ -3h + 24
Hence, answer is -3h + 24.
Car Survey 1500 In a survey of people who owned a certain type of car ,675 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
The percent of the people surveyed were satisfied with the car will
be 45%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Total number of people in a survey of car = 1,500
And, 675 people said they would buy that type of car again.
Now,
Total number of people in a survey of car = 1,500
And, The people surveyed were satisfied with the car = 675
Hence, The percent of the people surveyed were satisfied with the car is;
= 675 / 1500 x 100
= 0.45 x 100
= 45%
Thus, The percent of the people surveyed were satisfied with the car will
be 45%.
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Use the graph of y=f(x) to graph the function g(x)=f(x + 1)-3.
y = f(x)
4
Choose the correct graph of g below.
OA
OC.
B.
O D.
Q
Function g(x) is a translation of one unit to the left and 3 units down of f(x), then the correct option for the graph of g is B.
which is the graph of the transformed function?Here we start with a function f(x), and we also have the graph of this function.
And we want to find the graph of the function defined as:
g(x) = f(x + 1) - 3
Notice that:
g(x)= f(x + 1)
Is a translation of one unit to the elft of f(x).
g(x) = f(x) - 3
Is a translation of 3 units down of the graph of f(x).
Then:
g(x) = f(x + 1)- 3
Is a translation of one unit to the left and 3 units down.
With that in mind, we can see that the correct option for the graph of g(x) is option B.
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
Using the trigonometry ratio, he angle of elevation of the ramp to the nearest degree is 11°.
In the given question,
A ramp goes from a doorway of a building to the ground.
The end of the ramp connected to the doorway is 1 foot above the ground.
The distance along the ramp to the building is 5 feet.
We have to find the angle of elevation of the ramp to the nearest degree.
The distance is 5 feet.
The height is 1 foot.
To find the angle of elevation we used the trigonometry ratio.
According the trigonometry ratio, we know that tangent is the ratio between height and distance.
We can write it as
tan A=height/distance
Now putting the value
tan A=1/5
tan A=0.2
So A = arctan(0.2)
A = 11.30°
A ≈ 11°
Hence, the angle of elevation of the ramp to the nearest degree is 11°.
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Solve for r.
r/3 + 16 = 19
Answer:
r = 9
Step-by-step explanation:
Hello!
Solve for r by isolating the variable.
Solve for r[tex]\frac r3 + 16 = 19[/tex] Subtract 16 from both sides[tex]\frac r3 = 3[/tex] Multiply both sides by 3[tex]r = 9[/tex]The value of r is 9.
There are 40 students in class. 12 like pink best, 4 like yellow and the rest blue. What fraction of the class likes blue?
Answer: [tex]\frac{3}{5}[/tex]of the class like blue
Step-by-step explanation:
There are : 40 - 12 - 4 = 24 ( students like blue )
[tex]\frac{24}{40}[/tex]= [tex]\frac{3}{5}[/tex]
Jacob wants to prove that AFGH = A/KL using SAS.
He knows that FG = J and F = J. What additional
piece of information does he need?
The piece of information does he need is ∠F ≅ ∠J.
What is triangle?
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.
Properties of triangle?
A triangle has three sides, three angles, and three vertices.The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.The sum of the length of any two sides of a triangle is greater than the length of the third side.Given,
ΔFGH = ΔJKL
By SAS property of triangle;
[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex], FG ≅ JK
third property ,
∠F = ∠J
By SAS property at least two side their ratio must be equal and one angle.
[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]
∠F = ∠J
So, option A is correct.
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What must the value of x be in order to prove that
AEFG a AEHG by SSS?
The value of x will be= 90 degress.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
triangle 1= traingle290=90. perpendicularwith the help of sas propertyboth angles are equal.hence,The value of x will be= 90 degress.
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