The general form of exponential function is given below:
[tex]\begin{gathered} y=a.b^x+c \\ \text{When a.b}^x=0,\text{ the asymptote of the function becomes } \\ y\text{ = c , which is, y-intercept} \\ \text{But where c=0, the asymptote is the line y = 0} \end{gathered}[/tex]Expand 3(x - 1)(x + 4) and simplify.
Answer:
3x2-11x-4
Step-by-step explanation:
Combine the like terms to create a equivalent expression -4r - 2r + 5
After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.
As given in the question,
Given expression is equal to :
-4r -2r + 5
Now combine the like terms to get the equivalent expression we have,
Like terms of the given expression -4r -2r + 5 are -4r and -2r
( -4r -2r) +5
= -r (4+2) +5
= -6r +5
Equivalent expression of the given expression -4r -2r + 5 is -6r +5.
Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.
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HELP!!!
An area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds. How much food did she give each bird? The dividend is The divisor is . The division expreesion is Rewrite the division expression to get Each bird receives -cup of bird food.
Each bird would receive 1/9 cup of bird food.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given an area model with 12 shaded parts and 6 unshaded parts. The shaded part is labeled two-thirds. Adela divided Two-thirds of a cup of bird food equally among 6 birds.
The dividend would be
⇒ 2/3
The divisor would be
⇒ 6
The division expression would be
⇒ 2/3
Divided by 6
Rewrite the division expression to get
⇒ 2/3 × 1/6
⇒ 2 / 18
⇒ 1/9
Therefore, each bird would receive 1/9 cup of bird food.
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-23x^7 + x^9 -6x^3 + 10 + 2x^2
The polynomial is x⁹ - 23x⁷ - 6x³ + 2x² + 10 in the standard form, the degree of the polynomial is nine, and its leading coefficient is 1.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The polynomial below which is given in the question
-23x⁷ + x⁹ -6x³ + 10 + 2x²
To determine the polynomial in the standard form.
⇒ -23x⁷ + x⁹ -6x³ + 10 + 2x²
Rearrange the terms in the descending order of the degree of variables
⇒ x⁹ - 23x⁷ - 6x³ + 2x² + 10
This is the polynomial in the standard form
Here the degree of the polynomial is nine because nine is the highest degree in the above expression and its leading coefficient is 1.
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The question seems to be incomplete the correct question would be:
Write the polynomial in the standard form, and then identify the degree and leading coefficient
-23x⁷ + x⁹ -6x³ + 10 + 2x²
shelly sews a square blanket that has an area of 144 square feet. it has 36 square blocks, each the same size. what is the approximate length of each side of a block? (1 point)
The side of the square of each block = 2 feet
Given,
Shelly sews a square blanket that has an area of 144 square feet.
and, it has 36 square blocks, each the same size.
To find the approximate length of each side of a block
Now, According to the question:
36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks
= 144/ 36
= 4
The area of each square = 4 square feet
We know that
Area of square = side ^2
Side ^2 = 4
side = [tex]\sqrt{4}[/tex]
Side = 2
Hence, The side of the square of each block = 2 feet
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select all the equations that have the same solution as the equation 3x-12=24
The equation that have same solution to 3x-12=24 is 4x - 30 = 18.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The equation given is illustrated as:
3x - 12 = 24
Collect like terms
3x = 24 + 12
3x = 36
Divide through by 3.
3x / 3 = 36 / 3
x = 12
In this case, 4x - 30 = 18 will be:
4x - 30 = 18.
Collect like terms
4x = 18 + 30.
4x = 48
Divide
x = 48/4
x = 12
Therefore, 4x - 30 = 18 has same solution.
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what are the coordinates of the point on the directed line segment from (-7,-2) to (-2,8) that partitions the segment into a ratio of 3:2
The coordinates of the point on the directed line segment are (-4, 4).
What is partitions of the segment?
Finding a position that is an equal distance from A and b equal distance from B is necessary for partitioning a line segment, AB, into a ratio of a/b.
Trying to find the coordinates of point that splits the line between (-7, -2) to (-2, 8) at a ratio of 3:2.
Since the ratio is 3:2 we are going o find the point that is 3/5 of the distance from (-7, -2) to (-2, 8).
For the x coordinate, find the distance between x coordinates (-2-(-7)) = 5.
Take 3/5 of 5 equals to 3 and add that to the first x coordinate (-7) to get the x - coordinate of interest -4.
For the y - coordinate, find the distance between y coordinates (8-(-2)) = 10.
Take 3/5 of 10 equals to 6 and add that to to the first y coordinate (-2) to get the y coordinate of interest 4.
The coordinates of the point on the directed line segment from (-7, -2) to (-2, 8) that partitions the segment into a ratio of 3:2 are (-4, 4).
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2. LeRoy purchased 6 gallons of gasoline for
$19.56. Which describes the constant of
proportionality?
A.
B.
C.
D.
$2.26 per gal
$3.26 per gal
$3.29 per gal
$3.39 per gal
Factor completely... Please help me with this
Answer: (5x - 1)(x + 9)
Step-by-step explanation:
Please note the method of factoring may differ per class, but this is how I was taught.
First, we will multiply the coefficient of x² by the constant.
5 * -9 = -45
Next, we will find two numbers that add up to 44 (coefficient of x) and multiply to -45 (the number we got above).
-1 * 45 = 45
-1 + 45 = 44
-1 and 45 ✓
Now, we can start to factor. First, we will rewrite 44x.
5x² + 45x - 1x - 9
Then, we will factor by grouping.
5x(x + 9) -1(x + 9) ➜ (5x - 1)(x + 9)
The completely factored form is:
(5x - 1)(x + 9)
4x^2-5x-1. find the roots
Answer:
Please comment if it is wrong.
Which equation has no solution?
Answer:
1.)|4x-2|=-6
This eguation has not solution.
Answer:
the first one; absolute value cannot be negative
Step-by-step explanation:
|4x-2| = -6
add 2
|4x| = -4
divide 4 on both sides
x = -1
|4x-2| = 6
repeat the same steps
x = 2
A box, in the shape of a square pyramid, has a base side of 9 in. and a height of 15 in. What is the approximate volume of the box when it is 75% full? (Use V=
'Bh, where B is the area
of the base, and h is the height.)
The approximate volume of the pyramid when it's 75% full is 303.75 inches³.
How to find volume of a pyramid?The volume of a square base pyramid can be represented as follows:
volume of the square base pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore, the square bas pyramid has a base side of 9 inches and height of 15 inches. Let's find the volume when it's 75% full.
B = 9² = 81 inches²
h = 15 inches
Therefore,
volume of the square base pyramid = 1 / 3 × 81 × 15
volume of the square base pyramid = 81 × 5
volume of the square base pyramid = 405 inches³
Therefore, when it's 75% full
volume = 75% of 405
volume = 75 / 100 × 405
volume = 30375 / 100
volume = 303.75 inches³
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I WILL GIVE YOU BRAINLIST Show your work
11/2 divide by 3/4
if a child is 120cm tall, but they grow 4% bigger in a year, how tall will they be?
Answer
The height of the child in a year time = 124.8 cm
Explanation
The child is currently 120 cm tall.
The child grows 4% bigger in 1 year.
We now need to calculate how tall the child is in that 1 year.
New height for the child = (Current height) + (Increase in height)
Current height = 120 cm
Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm
New height for the child = (Current height) + (Increase in height)
= 120 + 4.8
= 124.8 cm
Hope this Helps!!!
Each person gets 3 scoops of ice cream. Is this relationship between the number of people and the number of scoops proportional?
Yes, the number of scoops proportional.
Define Proportional
A linear relationship between two amounts or variables is indicated by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Hence, It is proportional. This is because as the number of people increases, the number of scoops also increase.
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12. The length of one side of
a rectangle is
12cm.
The length of the diagnol of
the rectangle is 13cm
Calculate the area of the
rectangle
Answer :- 60 cm^2
Step-by-Step Solution :-
Let ABCD be the Rectangle.
Given :
AD = 12 cm
BD = 13 cm
To Find : Area of ABCD
Solution :
In ∆ADB,
AD = 12 cm and BD = 13 cm
By Pythagoras Theorem,
(BD)^2 = (AD)^2 + (AB)^2
13^2 = 12^2 + (AB)^2
169 = 144 + (AB)^2
AB^2 = 169 - 144 = 25
AB = √25
Therefore, AB = 5 cm
Now, to find the Area,
Area of Rectangle = length × breadth
Area of ABCD = 12 × 5
Therefore, Area of ABCD = 60 cm^2
the difference of t and five multiplied by six is four
The expression of the mathematical statement given as the difference of t and five multiplied by six is four is 6(t - 5) = 4
How to express the mathematical statement as an expression?From the question, the mathematical statement is given as
the difference of t and five multiplied by six is four
The difference of numbers means that we subtract the numbers
i.e. difference means subtraction
So, we have
the difference of t and five multiplied by six is four ⇒ (t - five) multiplied by six is four
The multiplication of numbers means that we take the product of the numbers
i.e. multiply means product
So, we have
the difference of t and five multiplied by six is four ⇒ (t - five) x six is four
Lastly, we have
(t - five) x six = four
Express as numbers
(t - 5) x 6 = 4
This becomes
6(t - 5) = 4
Hence, the expression represented by the statement is 6(t - 5) = 4
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A survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books.
Book Preference
Print Electronic
Youths 34 40
Adults 38 28
What percent of the youths surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
If a survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books. The percent of the youths surveyed prefer reading electronic books is: 54%
How to determine the percentage?Given data:
Youth book preference
Print = 34
Electronic = 40
Now let determine the percentage using this formula
Total = Print + Electronic book
Total = 34 +40
Total = 74
Now let determine the percentage of youth that preferred reading electronic book which is calculated as :
Percentage = 40 / 74
Percentage = 0.54 × 100
Percentage = 54 %
Therefore we can conclude that 54% like to read electronic book.
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The circle below is centered at (5,5). Use the graph to answer the following questions. please help!
Answer: I don't know why I'm here
Step-by-step explanation: help
m(x) = 4x + 15 m(x) needs to be 7 x =
Answer:
x = -2
Step-by-step explanation:
If m(x) = 4x + 15 and m(x) = 7, the we can substitute and get the equation:
4x + 15 = 7
x = -2
£ represents a group of 20 people that visited paris for a weekend break. 8 of the group visited the eiffel tower (ET) 13 of the group visited the no tre-dame cathedral (NDC) 5 of the group did not visit either of these places a person is chosen at random from the group. what is the probability that this person only visited one of the two places?
The probability that this person choosen only visited one of the two places is 9/20
What is Probability?
Probability is a measure of the possibility that an event to occur.
The probability for an event to occur= Possible outcome /Total outcome
to get the possible out come we must Know the number of people that visited ET and NDC only.
using set theory;
if x is the no of people that visited both places then,
8-x =ET only
13-x= NDC only
5= none visited ET and NDC
x+13-x+8-x+5=20
collect like terms
26-x= 20
x =6
therefore ET only= 2
NDC only= 7
probability of ET = 2/20
probability of NDC= 7/20
therefore probability that the person chosen only visited one place = p(ET)+P(NDC)= 7/20+2/20
= 9/20
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Which expression are equivalent when y=2 and y=5
The equivalent expressions when y = 2 and y = 5 are the expressions that have the same numeric value when y = 2 and when y = 5.
What are equivalent expressions?Equivalent expressions are expressions that have the same numeric value.
Hence, the equivalent expressions when y = 2 and y = 5 have the same value when y = 2 and y = 5.
This numeric value is calculated replacing each instance of y by 2 when y = 2 and each instance of y by 5 when y = 5.
For example:
2y + 3 at y = 2: 2(2) + 3 = 7.2y + 3 at y = 5: 2(5) + 3 = 13.Different numeric values, hence not equivalent, just an example as to how you should proceed.
You will do this for all expressions, and when you find equal values for y = 2 and for y = 5, then they will be equivalent.
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If you vertically compress the absolute value parent function, f(x) = Ixl, by afactor of 4, what is the equation of the new function?A. g(x)=xB. g(x) = 4xC. g(x) = 14x1D. g(x) = |x-41
Solution:
Given the absolute value parent function below
[tex]f(x)=|x|[/tex]If the function is vertically compressed by a factor of 4, the function becomes
[tex]g(x)=\frac{1}{4}f(x)[/tex]Where
[tex]\begin{gathered} f(x)=|x| \\ g(x)=\frac{1}{4}|x| \end{gathered}[/tex]Hence, the answer is
[tex]g(x)=\frac{1}{4}\lvert x\rvert[/tex]Option A
Describe how the equations for an ellipse, circle, hyperbola and parabola differ from one another. Include an example of each in your description.
See explanation below
Explanation:An ellipse has a standard equation formula written as:
[tex]\frac{(x^{}-h)^2}{a^2}+^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]When the sign between the x^2 and y^2 terms is positive, then it is a ellipse
[tex]\begin{gathered} \text{example of an ellipse:} \\ \frac{(x-3)^2}{9}\text{ + }\frac{(y\text{ - 8})^2}{25}\text{ = 1} \end{gathered}[/tex]An hyperbola has a standard equation written as:
[tex]\frac{(x^{}-h)^2}{a^2}-^{}\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]when the sign between the parenthesis of x^2 and y^2 terms is minus, then it is an hyperbola
[tex]\begin{gathered} \text{example of a hyperbola:} \\ \frac{x^2}{64}\text{ - }\frac{y\text{ }^2}{49}\text{ = 1} \end{gathered}[/tex]A circle has a general formula written as:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where vertex = (h, k)} \\ r\text{ = radius} \end{gathered}[/tex]The terms x^2 and y^2 are not divided by a constant. Also the left side of the equation represents the square of the radius
[tex]\begin{gathered} An\text{ example of a circle} \\ (x-1)^2+(y-3)^2\text{ = }10 \end{gathered}[/tex]Parabola has a vertex form of equation written as:
[tex]\begin{gathered} y=a(x-h)^2+\text{ k} \\ \text{where a = constant} \end{gathered}[/tex][tex]\begin{gathered} An\text{ example:} \\ y\text{ = 2(x - 1})^2\text{ + }3 \end{gathered}[/tex]Here, we only have term x^2, no y^2. y has an exponent of 1. Also a constant of a
Please help me with this
Answer:
1 and 3 makes linear pair
1 and 4 vertically opposite angle
1 and 5 are corresponding angle
1 and 8 alternate exterior angle
A jet ski rental charges a flat rate of $75, plus an additional $10 per hour. You only have $200 to spend. How many hours can you rent the jet ski?
PLS HELP ME
Answer:
12.5 hours
Step-by-step explanation:
The flat rate is the base, in which no matter how long you rent it for, they'll still charge you that much. You have 200 dollars, and negative 75 is 125 dollars, which you can spend on the hours. Assuming you can rent the jet ski for half an hour, you can divide 125 by 10 for the amount of hours, and the answer is 12.5 hours. However, if you can't rent the jet skis for half an hour, the answer is 12 hours.
A 21-foot bean is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If x represents the length of the first piece, find the length of each piece
Answer: 3, 9, and 9
Step-by-step explanation:
X+3x+3x=217x=21x=33, 9, 9=21
A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
4
25
32
200
The average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25 .
In the question ,
it is given that
the position of the particle that travels along the x-axis at time t is given by the function
x(t)=2t²+t
the average speed of the particle can be calculated by using the formula
average speed = (change is distance)/(change in time)
particle position at t=2
x(2) = 2(2)²+2 = 2*4+2 = 10
particle position at t=10
x(10) = 2(10)²+(10)
= 2*100+10
= 200+10
= 210
So, change in distance = 210-10= 200
change in time = 10-2 = 8
Putting the values in the average speed formula we get
average speed = 200/8
= 100/4
=25
Therefore , the average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25 .
The given question is incomplete , the complete question is
A particle travels along the x-axis such that its position at time t is given by the function x(t)=2t²+t . What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
(a) 4
(b) 25
(c) 32
(d) 200
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how do I simplify it to find the determinant in an easy way
The determinant of the given matrix is [tex]2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
Determinant of the matrix:
Determinant of the matrix is defined as a scalar value which is associated with the square matrix.
Given,
Here we have the matrix show in the question.
Now, we need to find the determinant of the matrix.
To find the determinant of the matrix we have to do the following steps:
1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.
2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.
This process can be elaborated in the following steps:
[tex]=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)[/tex]
When we expand the equation then we get,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)[/tex]
Group the similar terms and arrange them in order,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)[/tex]
Again we have to expand it and then we get,
[tex]= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4[/tex]
After the simplification, the resulting determinant is
[tex]=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
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What should be done to 5x^2 +15x in order to create a perfect square?
Answer:
To create a perfect square of given expression,
[tex]5x^2+15x[/tex]On solving the above expression we get,
[tex]=5(x^2+3x)[/tex]we have that,
[tex](x+a)^2=x^2+2ax+a^2[/tex]To create a perfect square: add ( half the coefficient of the x- term )²
Coefficient of x term is 3
half the coefficient of the x- term is 1.5
( half the coefficient of the x- term )² is 2.25
Add 2.25 to the quadratic expression inside the bracket, we get,
[tex]=5(x^2+3x+2.25)[/tex]In general, we adding 11.25 (that is, 2.25x5=11.25) to the given expression.
we get,
[tex]=5(x+1.5)^2[/tex]Multiply 5 to the above equation, we get
[tex]=5^2(x+1.5)^2[/tex][tex]=(5x+7.5)^2[/tex]Based on the above calculation, we adding 11.25 and multiplying the expression by 5 in order to create a perfect square.
Adding 11.25 and multiplying the expression by 5 in order to create a perfect square.