In one of the equations, separate one of the two variables. In the other equation, replace the expression with the value of the isolated variable from Step 1. Consequently, a linear equation with just one variable ought to emerge.
What constitutes the substitution system's solution?The one y-value in the substitution method is replaced with the other. We'll give an example to illustrate this. Since y = y, we can replace y in the second equation with y from the first equation. The linear system's solution is (1, 6).
What are the three possible types of solutions for a linear equation?Numerous solutions, no solutions, and a singular solution.
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A line that includes the points (k,
–
4) and (5,
–
2) has a slope of
–
1. What is the value of k?
The required value of k is 7 for a line that includes the points (k,–4) and (5,–2).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
As per the question, the slope of the line is -1, and the given points are (k, -4) and (5, -2).
So we can substitute these values into the formula:
-1 = (-2 - (-4)) / (5 - k)
-1 = 2 / (5 - k)
-1 × (5 - k) = 2
-5 + k = 2
k = 2 + 5
k = 7
Therefore, the value of k is 7.
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What is the volume of this rectangular prism?
Answer:
40
Step-by-step explanation:
5 x 4 x 2 = 40
length x width x height = volume
A license plate consists of 3 letters followed by 1 digit. How many license plates are possible if the first letter can be any letter except I or O, the digit cannot be 0, and no letters or digits may repeat
Answer:
85
Step-by-step explanation:
So you know that there are 26 letters in the alphabet and 3 letters in the license plate, so that would be 26 multiplied by 3 to cover all of those letters. The first letter can't be I or O, so you subtract 2 from the product. 26 times 3 is 78, minus 2 is 76. There are 10 single digits, but only one in the plate and it can't be 0. This leaves 9 digits so you add that to the total number.
76 + 9 = 85
I hope this helps! :)
Sorry for my previous answer, I misread the question, but this is the correct answer now, hope this helped!
Answer:
129600 license plates
Step-by-step explanation:
This time, we will use an option of solving where we take the number of possibilities for one letter, then multiply it by the next, then multiply it by the next, then multiply it by the number of possibilities for the number. We would have 24 letters to start (not including I or O), then after we pick one, we need to remove it since we can't repeat letters. So just for our letters, we would get:
24 * 25(only the first digit can't have I or O) * 24
Then, we need to multiply that by 9 (since we are not including 0), giving us:
24 * 25 * 25 * 9 = 129600
Meaning, we can have 129600 different license plates.
Hope this helped!
What is the equation of the line in slope-intercept form that has a slope of 6 and a y-intercept of 1/2
- I have struggled with this for an hour
-I have been taking tutoring and still need help -it's just not clicking
Explain a few ways that placing figures in a coordinate plane can be helpful for solving different problems.
Use the coordinate plane to graph points, lines, and geometric forms in the different quadrants, and then use the absolute value to determine the distances between them.
What does ordinate math entail?
An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Meaning of a Coordinate Plane. The intersection of the x-axis and y-axis, two perpendicular lines that form a 2D plane known as a coordinate plane.
Which three coordinate systems are there?
Cartesian, cylindrical, and spherical are the three most often used coordinate systems. We'll discuss a cylinder-based coordinate system as well as a cartesian-based one in this chapter.
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A frictionless pendulum is pulled 3 feet to one side of its center resting point…
A. The amplitude of the sinusoidal function 's' would increase.
B. The midline of the sinusoidal curve will upshift.
What is a periodic function?A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.
We are aware that a periodic function can be used to graph the pendulum's movement mechanism.
A. The pendulum will rise higher on both sides as it is drawn farther away from its resting point; this will result in an increase in the sinusoidal curve's amplitude.
B. The midline of the sinusoidal curve would rise up along the y direction as a result of an increase in magnitude if the pendulum was drawn further away from its resting point.
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Maria had lunch at a restaurant. If the bill was $12.25 and Maria wants to leave a 20% tip, what is a reasonable estimate for the amount she should leave for tip?
Please explain how you got the answer
Answer: $2.45
Step-by-step explanation:
An easy way to find the correct tip is to learn what 20% of 12.25 is
Let's convert the percentage to a decimal by moving the decimal point two spaces to the left. Now we have .2
.2 X 12.25 = 2.45
2.45 is 20% of 12.25
What is the circumference of a circle with sector area 9π and arc measure 90 degrees?
By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is
Circle area is equal to. πR² = 9π
Circumference =2πR
=> 2π*3 = 6π cm
Arc length equals (60/360)*6 to cm
Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 + π cm
Therefore , the solution of the given problem of circle comes out to be
6 + π cm.
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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
sector area of circle = 9π
arc measure = 90°
Area of sector = (arc/360°)*πr²
⇒ 9π = (90°/360°)πr²
⇒ 9π = (1/4)πr²
⇒ 4*9π = πr²
⇒ 36 = r²
⇒ 6² = r²
r = 6
and Circumference of circle = 2πr
=> 2π*6 = 12π cm
Therefore , the solution of the given problem of circle comes out to be
12π cm.
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SA triangle has side lengths of 11, 60, and 61. When using the converse of the Pythagorean theorem to determine if this is a right triangle, what is the value of c in the formula a² +b²=c²?
61
11
11²
60
Value of c is determined 61 unit.
What is right-angled triangle?
Triangle that has one angle 90 degree is called right-angled. In case of a right triangle the square of the largest side length is equal of the sum of the square of the other two side length.
what is the value of c in the above formula?
SA triangle has three side length 11-unit, 60 unit and 61 unit respectively.
The triangle is verified as a right-angled triangle by Pythagorean theorem.
And as the properties of a Pythagorean theorem the sum of the square of two side length is equal to the square of the largest side length.
if we say, one side length, a = 11 unit
second side length, b = 60 unit
the largest side length, c
now we will check,
√(11²+60²) = c² =√3721 = 61
the value of c = 61 unit.
hence, the SA is right-angled triangle.
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y
Which of the following best represents R = A - B?
A)
B)
R
The closing side of the triangle serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.
what is vector ?A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed geometrically, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or phenomenon known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.
given
As stated in the issue, we must determine the resultant vector by adding vectors A and B.
The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.
Option C is the proper response, thus.
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Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie
Bonnie will complete four laps before being passed by Annie because she runs an additional quarter lap for every lap she completes. This indicates that Annie and Bonnie are on an equal footing, and Annie must complete an additional lap to pass Bonnie. Annie will have completed five laps after that.
What unitary method examples are there?We can use the unitary method to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.
What circumstances allow us to use the unitary method in our daily lives?The unitary method can be used to calculate how many kilometres a car will travel on one litre of gas if it travels 44 km on two litres of fuel. In other words, the unitary method is the process by which we determine the value of a single unit and then use that information to determine the values of multiple units.
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what are the domain and range of the function f(x)=2^x+1
Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values
Step-by-step explanation:
Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and Range: (0,∞).
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : f(x)=[tex]2^{x}[/tex]+1
If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.
The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.
The values of its y-axis remain between 0 and. This is the set of y values, or the range.
However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.
The exponent's addition to 1 moves the function to the left without changing the range.
The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)
Range: (0,∞)
Therefore , the solution of the given problem of function comes out to be
Domain: (-∞, ∞) and Range: (0,∞).
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I NEED HELP!!
1ST QUESTION
a). 5 divided by 3/10
b.) 5 divided by 9/10
Answer:
a) 5 divided by 3/10
To solve this problem, we need to perform the division first, followed by the division. Dividing 5 by 3/10, we have:
5 / (3/10) = (5*10)/3 = 50/3
Simplifying, we have:
50/3 = 16 2/3
Therefore, the result of 5 divided by 3/10 is 16 2/3.
b) 5 divided by 9/10
To solve this problem, we need to perform the division first, followed by the division. Dividing 5 by 9/10, we have:
5 / (9/10) = (5*10)/9 = 50/9
Simplifying, we have:
50/9 = 5 5/9
Therefore, the result of 5 divided by 9/10 is 5 5/9.
Step-by-step explanation:
Answer:
a).5 divided by 3/10
= 16.6666666667
And,
b).5 divided by 9/10
=4.5
help me, please. I can't figure out if this is zero or infinite??
Answer:
it doesn't have any solutions bc the lines are parallel and don't share any points in common. hope this helps!
help ! what's the value of x -
[tex] {x}^{4} + 4 = 100 \div 5[/tex]
Answer:
2
Step-by-step explanation:
100/5 = 20
x⁴ + 4 = 20
x⁴ = 20 - 4
x⁴ = 16
= 2 × 2 × 2 × 2
x⁴ = 2⁴
x = 2
Hence, the value of x is 2.
i need help fr fr like my mind honestly went blank
Answer:
894 mi²
Step-by-step explanation:
the area of parallelogram= base x height= 24mi x 37.25mi = 894 mi²
Which statement about the order of operations is TRUE?
Complete all subtraction operations before addition.
Simplify operations within the innermost grouping symbols first.
Complete all division operations before multiplication.
Simplify exponents before operations in grouping symbols.
by using the distributive property and the greatest common factor what is 18+15
Answer:
33
Step-by-step explanation:
18 + 15 ← factor out 3 ( the GCF ) from each term
= 3(6 + 5)
= 3(11)
= 3 × 11
= 33
Points p and q are negative integers plotted on a number line. If |p| > |q|, which statement is true?
A. Point p is closer to 0 than point q, and to the right of point q.
B. Point p is closer to 0 than point q, and to the left of point q.
C. Point p is further from 0 than point q, and to the right of point q.
D. Point p is further from 0 than point q, and to the left of point q.
Point p is further from 0 than point q, and to the left of point q.
The correct option is D.
What is an absolute value?The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.
Given:
Points p and q are negative integers plotted on a number line.
And |p| > |q|.
That means,
The absolute value of p is greater than the absolute value of q.
|p| and |q| are the positive integers.
So, p < q.
So, the q is closer to zero.
And p is left to point q.
Therefore, the q is closer to zero and p is left to point q.
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help help help help help help
The equation point slope is y - y1 = m(x - x1)
we got y - (-16)=3(x-7)
what is meant by point of slope?Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-interceptThe slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept pointA simple definition of point-slope form is an equation of a line written using one point on the line and the slope of the line. The point form is written as (x,y) and the slope is the rise over run, or the ratio of the change in the y values over the change in the x valuesThe slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).To learn more about point of slope refers to:
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Which pairs of events are independent? Select all that apply.
Answer:the last one is right, because you cannot control when rain happens, or where at that matter.
How do you factor with 4 parts?
When a polynomial has four or more terms, the easiest way to factor it is to use grouping.
Grouping can be understand more better with an example:
for eg: factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:
Break up the polynomial into sets of two. You can go with (x^3 + x^2) + (–x – 1). Put the plus sign between the sets, just like when you factor trinomials. The square x2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x^2(x + 1) – 1(x + 1).one can Factor again as many times as you can. The two terms you’ve created have a GCF of (x + 1). When factored out, you get (x + 1)(x^2 – 1).However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).
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Aida, Bernado and Cristiano need $30000 to start a business. a I They borrow & of this amount.
Show that they still need $18000.
They provide the $18000 themselves in the ratio
Aida: Bernado : Christiano = 5: 4: 3.
Calculate the amount each of them provides.
b i Office equipment costs 35% of the $30000.
Calculate the cost of the equipment. ii Office expenses cost another $6500.
Write this as a fraction of $30 000.
Give your answer in its lowest terms. iii How much remains of the $30000 now?
c They invest $12500.
After one year this has increased to $15500.
Calculate this percentage increase.
Answer:
aida:$7500
Bernardo:$6000
Christiano :$4500
b.i $10500
b.ii 13/60
b.iii $13000
c. 24%
I don’t know help m/12-8=4
Answer:
[tex] \frac{m}{12} - 8 = 4 \\ \frac{m}{12} = 4 + 8 \\ m = 12×12 \\ m = 144[/tex]
Hope it will help u...
Abraham ran 3.18 miles on Monday. On Tuesday, he ran 1.6 times further than he did on Monday. How many more miles did he run on Tuesday than on Monday?
1.908 miles Abraham run on Tuesday than on Monday.
How miles more miles he run on Tuesday than on Monday?Step 1
Monday he run 3.18 miles
Tuesday he run 1.6 times than Monday
how many more miles miles he run?
Step 2
3.18*(1.6-1)
1.6-1 is 1.6 times further than he did on Monday
Step3
3.18*(1.6-1)
=3.18*0.6
=1.908
he run on Tuesday than on Monday is 1.908
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Abraham ran 1.908 more miles on Tuesday than it was on Monday, based on the information provided.
Why is math referred to as arithmetic?The fundamental ideas in number theory, measurement, and computation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number") (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
First, he ran 3.18 miles on Monday.
He ran 1.6 times more on Tuesday than on Monday.
how many kilometers did he run in total?
Step 2\s3.18*(1.6-1) (1.6-1)
One and a half times closer than he was on Monday at 1.6-1
Step3\s3.18*(1.6-1)\s=3.18*0.6\s=1.908
He ran 2.908 more on Tuesday than it does on Monday.
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6. If sin θ = - 3/5and the terminal side of θ lies in quadrant III, find cosθ .
When sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is -4/5
What is terminal side of an angel?The terminal side of an angle refers to the line that intersects the initial line to make an angle
In the problem the terminal side is said to be in the third quadrant and the in the third quadrant sin θ = - 3/5
sin θ = opposite / hypotenuse
using Pythagoras the adjacent is 4, in third quadrant we have -4
cos θ = - adjacent / hypotenuse = -4/5.
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What does an inverse function look like?
Inverse functions are indicated by the symbol [tex]f^{-1}[/tex] and are functions whose inverse is the function itself (x).
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The inverse function, which also returns the beginning value, returns the result of a function.
The relationship that results from swapping out an independent variable for a variable that depends on a given equation, and which may or may not be a function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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find the missing angle
Answer:
Step-by-step explanation:
180-120=60
60+50=110
180-110=70
the missing angle is 70 degrees
2. Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192. How many hours did he work for each job?
Max mowed the lawns for 6 hours and tutored students for 8 hours.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192.
We can write the system of equations as -
x + y = 14
12x + 15y = 192
Refer to the graph attached. On solving the equation graphically, we get-
x = 6, y = 8
Therefore, Max mowed the lawns for 6 hours and tutored students for 8 hours.
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For how many integer values of $n$ between 1 and 349 inclusive does the decimal representation of $\frac{n}{350}$ terminate
The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.
What is prime factorization?The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.
Here,
first, find the prime factorization of 350. (2*5^2*7)
then we need to find all multiples of 7 that are between 1 and 350.
the first multiple of 7/350.
The first multiple of 7 between 1 and 350 is 7.
so 7/350=0.02.
Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.
Then, we get 49.
49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.
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