The equation of the line passing through the given point that is
parallel to the given lines are;
16) y = ²/₃x + 6
17) y = ²/₇x - 1
18) y = ³/₄x - 11
19) y = -4x + 12
What is the equation of the Line?
16) We are given the equation of a line as;
y = ²/₃x - 2
The general equation of a line in slope intercept form is ;
y = mx + c
where;
m is slope
c is y-intercept
Thus, equation passing through (-3, 4) is;
y - 4 = ²/₃(x - (-3))
y - 4 = ²/₃x + 2
y = ²/₃x + 6
17) We are given the equation of a line as;
-2x + 7y = 14
7y = 2x + 14
y = ²/₇x + 2
Thus, equation passing through (-7, -3) is;
y - (-3) = ²/₇(x - (-7))
y + 3 = ²/₇x + 2
y = ²/₇x - 1
18) We are given the equation of a line as;
3x - 4y = 16
4y = 3x - 16
y = ³/₄x - 4
Thus, equation passing through (8, -5) is;
y - (-5) = ³/₄(x - 8)
y + 5 = ³/₄x - 6
y = ³/₄x - 11
19) We are given the equation of a line as;
4x + y = 7
y = -4x + 7
Thus, equation passing through (2, 4) is;
y - 4 = -4(x - 2)
y - 4 = -4x + 8
y = -4x + 12
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what number multiplied by 23 as a product of 1
The number that should be multiplied by 2/3 to get a product 1 is 3/2
What is the Reciprocal of two numbers?
One of two numbers that, when multiplied together, equals to 1 is known as a reciprocal or multiplicative inverse.
Transposing the numerator and denominator will allow you to get the reciprocal if you can reduce the number to a fraction.
Let the number that would result in product 1 be "x"
So, According to the question:
=> x × 2/3 = 1
Solving for x,
Dividing by 3/2 both sides
⇒x = 3/2 which is the reciprocal of 2/3
Hence,
The number that should be multiplied is 3/2
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Is ABCD a rhombus explain?
The ABCD parallelogram turns into a rhombus if all of its sides are equal.
What are the geometric properties of a parallelogram and a rhombus?Geometry of a parallelogramEqual are the sides that oppose.Equal angles are opposite angles.Each other in a diagonal.Nevertheless, the length of diagonals varies.Geometric characteristics of rhombusAll Sides are equal.
Diagonals bisect at 90°.
In our question,
AB = DC is given for a quadrilateral ABCD (parallelogram).
When a parallelogram's sides are uneven, symmetry is disrupted and its diagonals do not bisect at 90 degrees. However, when all of the sides are equal, the diagonal does bisect at 90 degrees and the parallelogram becomes a rhombus.
Therefore, when all of a parallelogram's sides are equal, it becomes a rhombus.
The complete question is:
You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?
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Find the amount Erica owes at the end of 6 years if $ 5300 is loaned to her at a rate of 8 % compounded monthly. use A=P(1+r÷n)ⁿt
The amount owed is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest as given in the questions is
A = Final amount P = principalr = ratet = timen = number of times compoundedA = P[(1 + r/n)^nt
Substituting the values into the formula
A = 5300(1 + 0.08/6)^12 * 6
A = 8,551.56
Erica will owe $8551.56
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How do you define a function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).
The metaphor of a function machine, which accepts an object as its input and produces another object as its output based on that input, makes the concept of a function simple to understand.
Given a collection of possible outputs Y (codomain) and a set of inputs X (domain), a function is more precisely defined as f: X→Y which shows that f is a function from X to Y using this notation.
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The admission fee at a local zoo is $1.50 for children and $5.00 for adults. On a certain day, 3700
people enter the zoo and
$11, 500.00 is collected. How many children and how many adults
attended?
How many children attended?
How many adults attended?
The table shows the lengths of hiking trails. It took Lannie 1.9 hours
to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.
Write and solve an equation to find the average hiking rate for
Lannie. Write and solve an equation to find the average hiking rate
for Ava. What is the difference between their average hiking rates?
Round to the nearest tenth.
The difference between their average hiking rates is 0.51 miles/hour.
Given that, it took Lannie 1.9 hours to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Using speed =Distance/Time
Here, Ranger Cove distance =4.8 miles and time =1.9 hours
Now, rate =4.2/1.9
= 2.21 miles/hour
Mohawk Trail distance =6.8 miles and time =4 hours
Now, rate =6.8/4
= 1.7 miles/hour
The difference between their average hiking rates
= 2.21-1.7
= 0.51 miles/hour
Hence, the difference between their average hiking rates is 0.51 miles/hour.
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A parachutist's rate during a free fall reaches 216 kilometers per hour. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 20 seconds of free fall? Do not round your answers.
Rate:
Distance fallen in 20 seconds:
The free fall speed of a parachutist can exceed 216 kilometres per hour. During his 20 seconds of free fall, the parachutist will plunge 1960 metres.
What is Acceleration ?Every time an object is subject to a net force that is greater than zero, acceleration happens. You can experience it when riding down a steep hill on your sled in the snow or when you slightly accelerate or decelerate in an elevator. Furthermore, we know that the universe as a whole is expanding at an even faster rate because to the general theory of relativity. This implies that the distance between two places is always enlarging, yet we are oblivious to this on a daily basis because every scale in the universe also expands.
During free only acceleration due to gravity(g) acts on the parachutist. Assuming acceleration due to gravity is positive i.e. g=9.8m/s² .
For conversion we know that
1 km = 1000 m and
1 hr = 3600 seconds
216 km/hr = 60 m/s
Location of parachutist during 20 seconds
[tex]h = \frac{1}{2} \times g \times t^2[/tex]
[tex]h=\frac{1}{2} \times 9.8 \times 20^2[/tex]
h = 1960 meters
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what is the fourth term of d 4b3
The fourth term of the polynomial (d - 4b)³ is D. -64d³.
What is a polynomial?A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.
Given the expression (d - 4b)³, we need to open the bracket, hence:
(d - 4b)³ = d³ + 3(d²)(-4b) + 3(d)(-4b)²
= d³ - 12bd² + 48b²d - 64d³
Therefore, the fourth term of (d - 4b)³ is D. -64d³
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How do you find the slope of a vertex?
How to find a parabola's equation using its Vertex Form
Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)2+k. ...
Step 2: find the value of the coefficient by substituting the coordinates of point P into the equation written in step 1 and solving for a.
Choose the symbol that correctly compares these numbers.
18.6? 18.7
O A. <
OB. =
O C. >
Answer: A
Step-by-step explanation:
18.6 is less than 18.7
so 18.6<18.7
write to show how you make a ten then add
A method for deriving facts is to multiply by 10 or to add using 10. This means that before using the make-ten strategy, kids need to know some facts by hear. Use of a make 10 strategy requires knowing that 8+2=10 and 9+1=10. In order to use the make 10 strategy, add 8 and 5, then decompose 5 into 2 and 3.
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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A quality control activity analysis indicated the following four activity costs of a hotel. Verifying credit card information $189,800 Customer service training 379,600 Discounting room rates due to poor customer service 94,900 Correcting charges to customer invoices 284,700 Total $949,000
The percentage of the quality cost, that is taken up by the prevention and appraisal costs are:
Prevention cost - 40%Appraisal cost - 20%How to find the percentage of cost?The prevention cost would be the cost associated with customer service training as this ensures that less mistakes are made.
The appraisal cost would be the cost to verify credit card information.
The percentage of total quality control cost that prevention cost is, would be:
= 379, 600 / 949, 000 total
= 40 %
The percentage for appraisal cost is:
= 189, 800 / 949, 000
= 20 %
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The rest of the question is:
Present the percentage values of prevention and appraisal as a percentage of the quality cost.
what is the length of ac brainly
The length of AC is equal to 5 units.
Given:
From the figure :
ΔABC is a right angled triangle with sides:
AB = 3 and BC = 4
Right angled triangle:
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.
The third side is called the hypotenuse, which is the longest side of all three sides.
we know that,
According to pythagorean theorem:
[tex]AB^2+BC^2 = AC^2[/tex]
3^2 + 4^2 = AC^2
9 + 16 = AC^2
AC^2 = 25
AC = [tex]\sqrt{25}[/tex]
AC = 5 units.
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Full question:
is in the image uploaded
Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the points
from your table.
y=-3x - 4
X
-1
0
1
y
The complete table of values of the linear equation y = -3x - 4 is
x y
-1 -1
0 -4
1 -7
How to complete the table of values?From the question, we have the following parameters that can be used in our computation:
y = -3x - 4
Also, we have the following table of values
x y
-1
0
1
The above table of values mean that the x values are
x = -1, 0 and 1
Substitute x = -1, 0 and 1 in the equation y = -3x - 4
So, we have the following representation
When x = -1
y = -3(-1) - 4 = -1
When x = 0
y = -3(0) - 4 = -4
When x = 1
y = -3(1) - 4 = -7
So, we have the following ordered pairs
(-1, -1), (0, -4) and (1, -7)
When represented on the table of values, we have
x y
-1 -1
0 -4
1 -7
The above represents the complete table of values
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What is the sum of 2 5 and 1/4 in fraction?
Gert invested all of her money at the end of 2000. At the end of each year, she checks the value of her investment. At the end of what ear will she first find she's doubled her money if gert invested all of her money at 5% simple interest?
The year in which Gert will find that she has doubled her money is year 20.
What year will the amount have doubled?
Simple interest is when the interest earned on an investment increases linearly each year.
The formula that can be used to determine simple interest is:
Simple interest = amount invested x duration of the investment x interest rate.
When the amount of money in the account is double what it is now, it means that the interest earned would be $2000 and the value of the account would $4000 (2000 + 2000).
Year when investment would have doubled = simple interest / (amount invested x interest rate)
Year when investment would have doubled = $2000 / (0.05 x 2000)
Year when investment would have doubled = $2000 / 100 = 20 years
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¿cuál es el área en cm² de la base de un prisma que tiene una altura de 51 cm y un
volumen de 245,8 cm³?
Respuesta:
On solving the given question, we got Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2
What is a prism?A prism is a polyhedron in geometry that has an n-sided polygonal basis, a second base that is a shifted version of the first base, and n additional faces—necessarily all parallelograms. Connect the matching sides of the two bases.
h = 51 cm
a = 2cm
therefore,
volume of a Triangular Prism = (½) abh cubic cm
245.8 = [tex]\frac{1}{2}[/tex] X 2 X b X 51
[tex]= > b = \frac{245.8 X 2}{2 X 51}[/tex]
[tex]= > b = \frac{491.6}{102}[/tex]
[tex]= > b = 4.819[/tex]
Now Area of base of prism
Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2
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degree of polynomial function examples
Examples of one variable polynomial:
• Zero polynomial: 3
The degree of the polynomial is not defined
• Constant polynomial: f(x)= 3
The degree of the polynomial is 0
• Linear polynomial: f(x)= 3x
The degree of the polynomial is 1
• Quadratic polynomial: f(x)= 2x^2+3-1
The degree of the polynomial is 2
• Cubic polynomial: f(x)= 3x^3-5x+2
The degree of the polynomial is 3
• Quartic polynomial: f(x)= 5x^4-6x^2+2x+3
The degree of the polynomial is 4
Example of multiple variable polynomial:
Polynomial: f(x)= 5x^4y^2z^3+3x^2yz+2xz
The degree of the polynomial is 9.
Degree of the polynomial:
The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial. The degree denotes the polynomial's highest exponential power.
Types of polynomial:
• Zero polynomial
• Constant polynomial
• Linear polynomial
• Quadratic polynomial
• Cubic polynomial
• Quartic polynomial
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Mia needs to bring at least 25 pieces of fruit to the school picnic. She is bringing both apples and oranges, and was told to be sure to bring more than 10 apples. Let x represent the number of apples and y represent the number of oranges. Select all inequalities that model this situation.
All the inequalities that model the given situation are;
x + y ≥ 25
x > 10
y > 0
How to solve Inequality word problems?
We are told that;
x represents the number of apples.
y represent the number of oranges.
Now, Mia needs to bring at least 25 pieces of fruit to the school picnic. Thus, the inequality is expressed as;
x + y ≥ 25
She is bringing both apples and oranges, and was told to be sure to bring more than 10 apples. Thus, the inequality is expressed as;
x > 10
Since we are not told the maximum number of oranges, then we can say it must be more than zero and as such we have the third inequality as; y > 0
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3(2x - 5) = 9(10 - x)
Answer:
x=7
Step-by-step explanation:
3(2x-5)=9(10-x)
6x-15=90-9×
6x+9x=90+15
15x=105
×=7
Answer:
x = 7
Step-by-step explanation:
1. Distribute
3(2x - 5) = 9(10 - x)
6x - 15 = 9(10 - x)
2. Rearrange Terms
6x - 15 = 9(10 - x)
6x - 15 = 9(-x + 10)
3. Distribute
6x - 15 = 9(-x + 10)
6x - 15 = -9x + 90
4. Add 15 to both sides
6x - 15 = -9x + 90
6x - 15 + 15 = -9x + 90 + 15
5. Simplify
Add the numbers:
6x - 15 + 15 = -9x + 90 + 15
6x = -9x + 90 + 15
Add the numbers:
6x = -9x + 90 + 15
6x = -9x + 105
6. Add 9x to both sides
6x = -9x + 105
6x + 9x = -9x + 105 + 9x
7. Simplify
Combine like terms:
6x + 9x = -9x + 105 + 9x
15x = -9x + 105 + 9x
Combine like terms:
15x = -9x + 105 + 9x
15x = 105
8. Divide both sides by the same factor
15x = 105
15x/15 = 105/15
9. Simplify
Cancel terms that are in both the numerator and denominator:
15x/15 = 105/15
x = 105/15
Divide the numbers:
x = 105/15
x = 7
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What does an exponential decay model look like?
Exponential decay graph looks like see the given image attached.
What is exponential decay?The process of diminishing an amount by a constant percentage rate over time is known in mathematics as exponential decay. The quantity drops gradually, followed by a dramatic decline in the rate of change and growth over time.
A linear function reduces the original number by the same amount each time, but exponential decay reduces the original amount by a constant percentage over time. Exponential decay differs from linear decay in this way: the decay factor depends on a percentage of the original quantity.
The exponential decay formula is used to determine this decline in growth.
Formula of exponential decay is given by
Its graph is given by
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Consider the expression 4x^2+x+34x 2 +x+34, x, squared, plus, x, plus, 3. Complete 222 descriptions of the parts of the expression.
[tex]72x^{2}+3x+3[/tex]Answer:
Step-by-step explanation:
[tex]1. (4x^{2}+34x^{2} +34x^{2} )+(x+x+x)+3\\ 2. 72x^{2} +3x+3[/tex]
Ms. Rios mowed
1
4
of her lawn. Her son mowed
3
7
of it. Who mowed most of the lawn? How much of the lawn still needs to be mowed?
Her son mowed the most lawn
35%of the lawn meeds to be mowed
Solve the compound inequality 1/2 x − 4 < 3 and 7 ≤ 3x + 5.
[tex] \frac{1}{2} x - 4 < 3 \\ [/tex]
Add both sides 4
[tex] \frac{1}{2} x - 4 + 4 < 3 + 4 \\ [/tex]
[tex] \frac{1}{2} x < 7 \\ [/tex]
Multiply both sides by 2
[tex]2 \times \frac{1}{2} x < 2 \times 7 \\ [/tex]
[tex]x < 14[/tex]
_____________________________________________
[tex]7 \leqslant 3x + 5[/tex]
[tex]3x + 5 \geqslant 7[/tex]
Subtract both sides minus 5
[tex]3x + 5 - 5 \geqslant 7 - 5[/tex]
[tex]3x \geqslant 2[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} \geqslant \frac{2}{3} \\ [/tex]
[tex]x \geqslant \frac{2}{3} \\ [/tex]
A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 13 minutes there are 630 bacteria, after how many minutes will there be 20 bacteria remaining?
When solving this problem, round the value of k to four decimal places and round your final answer to the nearest whole number
The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081
What is exponential function?An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.
The No of bacteria left at a particular time t is given as N(t)= Noe^-kt
where No= initial number of bacteria
k= decay constant and t = time
after 13 minutes
630= 700e^-13k
divide both sides by 700
630/700= e^-13k
0.9= e^-13k
ln0.9= -13k
k= ln0.9/-13 = -0.1054/-13 = 0.0081
time for 20 bacteria to be left =
20= 700e^-0.0081t
= 20/700=e^-0.0081t
0.0286= e^-0.0081t
ln0.0286= -0.0081t
-3.554= -0.0081t
divide both sides by -0.0081
t= -3.554/-0.0081= 439 minutes ( nearest minutes)
therefore the time for the bacteria to be left is 439minutes
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Question 1: Multiply: 12.10²
A 120
B 12000
c 1200
D 1.2
Am pula mare!
Da aaaaaaaaaaa????
The 2148 guests at a hotel have the choice to either go on a boat tour or go scuba diving. people decided to go scuba diving. people decided to neither scuba dive nor go on a boat tour. Each boat holds people. How many boats are needed?
The number of boats needed for 1491 people are 20.
What is the cross-product?
The cross product, also known as the vector product in mathematics, is a binary operation on two vectors in a Euclidean vector space that is oriented in three dimensions. It is represented by the symbol times.
We have,
134 people decided to go scuba diving,
523 people decided to neither scuba dive nor go on a boat tour,
So, people go to boat tour = 2148 -(134 + 523)
= 2148 - 657
= 1491
now, since each boat holds 78 people.
[tex]\frac{1491}{78} = 19\frac{3}{26}[/tex]
= 20 boats.
Hence, the number of boats needed for 1491 people are 20.
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Complete Question
The 2148 guests at a hotel have the. the choice to either go on a boat tour or go scuba diving. 134 people decided to go scuba diving. 523 people decided to neither scuba dive nor go on a boat tour. Each boat holds 78 people. How many boats are needed? Explain your reasoning.
How do I calculate a fraction of a fraction?
Multiply the fraction's bottom numbers with the top numbers in the two fractions.
The two fractions' top numbers should be multiplied, as should the bottom numbers.
Find the fraction of the following two fractions, for instance:
2/3, and 4/5
= 2/3 × 4/5
= (2×4)/(3×5)
= 8/15
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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please help!!!
A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
9 + 20p ≤ 125
Step-by-step explanation:
This does not include the tax.
At this rate, if Candidate A received 45 votes, how many votes did Candidate B receive?
The number of votes that Candidate B received, given the rate and the votes received by Candidate A, is 63 votes
How to find the number of votes?The question shows that for every 5 votes received by Candidate A, Candidate B will receive 7 votes.
This means that if Candidate A has 45 votes, the number of votes that Candidate B would receive can be found to be :
= Number of votes received by Candidate A / Number of votes Candidate A receives per Candidate B x Number of votes Candidate B receives per Candidate A
= 45 / 5 x 7
= 9 x 7
= 63 votes
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The first part of the question is:
Candidate A receives about 5 votes for every 7 votes received by Candidate B.
