The solution to the system of equations is (1, 8).
How to evaluate the system of equationsFrom the question, we have the following parameters that can be used in our computation:
y-x=7 y=3x+5
To find the solution to the system of equations y - x = 7 and y = 3x + 5, we can substitute the second equation into the first equation to eliminate y:
y - x = 7
y = 3x + 5
Substituting y = 3x + 5 into the first equation:
3x + 5 - x = 7
2x = 2
x = 1
Now that we have found x = 1, we can substitute it back into either equation to find y:
y = 3x + 5
y = 3 * 1 + 5
y = 8
So the solution to the system is (x, y) = (1, 8).
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Please answer I need help
Answer: C- Opposite sides are parallel. (Same distance apart)
Hope this helps :)
What kind of system is involved when the solution of a system of equation is the intersection of two lines?
The unique solution system is given by the intersection of two lines .
When the line intersects at a point the value of the function becomes zero and also intersecting lines meet at only one point.
Hence this type of system have a unique solution.
The condition of the unique solution is
a1/a2[tex]\neq[/tex]b1/b2
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Write the equation in Slope Intercept Form. y+
Find the geometric mean between each pair of numbers.
3√7 and 6√7
The geometric mean—also known as the compounded annual growth rate—is used to determine average growth rates.
What is meant by geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.
The geometric mean is a calculation that averages all values and determines the number's root. You must determine the nth root of the product of each integer in a set of n numbers. To summarise your data, utilise this descriptive statistic.
In finance, the geometric mean—also known as the compounded annual growth rate—is used to determine average growth rates.
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Please Help Me Fast!!!
A football is kicked from the ground and travels at a rate of 10 meters per second. The function y = 10x - 5x^2 represents the ball's height above the ground at x seconds.
a.) Use the given equation to determine how long after the football is kicked will it hit the ground?
b.) Graph the function.
What is the football's highest point?_______
How long did it take to get there?__________
The final statement is: a) the ball hits the ground after 2 seconds b) the highest point is 5 m 3) It takes t=1 to reach the highest point.
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The height is given by y=10x-5x²
When height y=0 therefore
0=10x-5x²
5x²=10x
5x=10
x=2
The ball hits the ground after 2 seconds and the highest point is at t=1
with maximum height=5 m
Hence, the graph reaches its maximum point at (1,5)
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Alan saved 55$. He has already spent 15$. He plans to spend 5$ on a movie ticket each month. Which inequality represents the name of movie tickets he can buy? solve the inequality.
15+5x<55 is inequality represents the name of movie tickets he can buy.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Alan saved 55$.
He has already spent 15$.
Alans plans to spend 5$ on a movie ticket each month.
We have to write the inequality which represents the name of movie tickets he can buy.
15+5x<55
Here x represents the number of movies he can watch
5x<30
x<6
Hence, 15+5x<55 is inequality represents the name of movie tickets he can buy.
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Solve for m/A
D
m/A =
A
{5x+18}°
(3x + 10)
C
B
When a variable can be substituted with a number to produce a true number statement, that number is the solution to the equation.
x = 10m - 1800° ACB / A(10A5 - 540° CB): 10A5 + 540° CB ≠ 0.
How to find the Calculation?m/A = A {5x+18}° (3x + 10) C B
m/A = A5x + 18° (3x + 10 )CB : x = 10m - 1800° ACB / A(10a5 + 540° CB;
10A5 + 540° CB ≠ 0
m / A = A5x + 18° (3x + 10)CB
A5x + 18°(3x + 10)CB = m/A
A5x. 10 + 18° (3x + 10)CB.10 = m/A .10
18°(3x + 10)CB . 10 : 180° CB(3x + 10)
m/A.10 : 10m/A
A5x. 10 + 180° CB(3x + 10 ) 10m/A
A5x. 10 + 180° CB(3x + 10) = 10m/A
A5x.10+180° CB (3x + 10) : 10A5x + 540° CB x + 1800° CB
A5x . 10 + 180° CB(3x + 10)
=10A5x + 180° CB(3x + 10)
180° CB(3x + 10); 540° CBx + 1800° CB
= A5x . 10 + 540° CBx + 1800° CB
10A5x + 540 ° CBx + 1800° CB = 10m / A
Move 180° CB to the right side
10A5x + 540° CBx = 10m / A -1800° CB
Factor 10A5x + 540° CBx : x(10A5 + 540° CB)
10A5x + 540° CBx
= x( 10A5 + 540° CB)
x(10A5 + 540° CB) = 10m /A - 1800° CB
x(10A5 + 540° CB) / 10A5 + 540° CB = 10m / A / 10A5 + 540° CB - 1800° CB / 10A5 + 540° CB: 10A5 + 540° CB ≠ 0
Simplify
x = 10m - 1800° ACB / A(10A5 - 540° CB): 10A5 + 540° CB ≠ 0.
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A box of cookies costs $4. Freeman has $34. The inequality below can be used to find the
numbers of boxes of cookies, x, Freeman can buy with $34.
4x ≤ 34
Which statement describes all the possible numbers of boxes of cookies Freeman can buy
with $34?
Answer: The inequality 4x ≤ 34 can be used to find the numbers of boxes of cookies, x, Freeman can buy with $34. The statement "x is a whole number less than or equal to 8.5" describes all the possible numbers of boxes of cookies Freeman can buy with $34.
Because 34 ÷ 4 = 8.5, Freeman can buy 8 boxes of cookies at most. Since x is the number of boxes, x is a whole number so Freeman can buy 8 boxes of cookies or less.
Step-by-step explanation:
annual sales for a company are $149,999 and are increasing at a rate of 5% per year. write an exponential growth function to model this situation. then, find the annual sales after 7 years.
The population of a city decreases by 1.8% per year. If this year's population is 396,000, what will next year's population be, to the nearest individual
Answer: 388872
Step-by-step explanation: take 396000 divide it by 98.2%
Given the following table, find the domain and range of the function.
=======SELECT ALL THAT APPLY PLEASE =======
A) domain: {2, 4, 5, 9}
B) range: {2, 4, 5, 9}
C) range: {-3, 1, 5, 7}
D) domain: {-3, 1, 5, 7}
SELECT ALL THAT APPLY
Solve.
524 people watch the town parade. 178 of them
are children. How many people watching the parade
are adults? For 3rd grade math
To find out how many people watching the parade are adults, we can subtract the number of children from the total number of people.
524 people - 178 children = 346 adults
So, 346 people watching the parade are adults.
Answer:
To find out how many people watching the parade are adults, we have to subtract the number of children from the total number of people.
Total number of people watching the parade: 524
Number of children watching the parade: 178
524 - 178 = 346
Therefore, 346 people watching the parade are adults.
question 4 please answer
On the graph above, the input when f(x) = -5 is equal to -2.
How to calculate an equation of this line?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear equation representing the line and passes through the points (-1, -2) and (1, 4) by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-2) = (4 - (-2))/(1 - (-1))(x - (-1))
y + 2 = 6/2(x + 1)
y = 3(x + 1) - 2
y = 3x + 3 - 2
y = 3x + 1
When y = -5, the input value (x) can be calculated as follows;
y = 3x + 1
-5 = 3x + 1
3x = -5 - 1
3x = -6
x = -6/3
x = -2.
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What is the interest earned in a savings
account after 12 months on a balance of
$1000 if the interest rate is 1.5% APY
compounded yearly?
interest $[?]
Round your answer to the nearest hundredth.
=
The interest earned in a savings account after 12 months on a balance of $1000, with an interest rate of 1.5% APY compounded yearly, is $15.00.
What is savings account?A savings account is a type of bank deposit account that typically pays interest and allows customers to access their funds at any time. Savings accounts are a safe, convenient way to store money, and they offer a variety of benefits, including allowing customers to earn interest on their deposits, access their funds quickly and securely, and take advantage of certain tax benefits.
This is calculated by multiplying the principal balance ($1000) by the interest rate (1.5%) and then multiplying by the number of years (12). Therefore, the interest earned is calculated as follows:
$1000 x 1.5% x 12 = $15.00.
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Write the first five terms of each sequence.
.
1.a(1) = 1, a(n) = 3-a(n-1), n ≥ 2
2. b(1) = 1, b(n) = -2+b(n-1), n ≥ 2
3. c(1) = 1, c(n) = 2 c(n-1) +1, n ≥ 2
4. d(1) = 1, d(n) = d(n-1)² + 1, n ≥ 2
5. f(1) = 1, f(n) = f(n-1) + 2n - 2, n ≥ 2
This is a sequence of numbers where each number is determined by the number that comes before it.
Write the first five terms of each sequence?a(1) = 1, a(2) = 2, a(3) = -1, a(4) = -4, a(5) = 7
b(1) = 1, b(2) = -1, b(3) = -3, b(4) = -5, b(5) = -7
c(1) = 1, c(2) = 3, c(3) = 7, c(4) = 15, c(5) = 31
d(1) = 1, d(2) = 2, d(3) = 5, d(4) = 26, d(5) = 677
f(1) = 1, f(2) = 3, f(3) = 6, f(4) = 11, f(5) = 18
The first number in the sequence is given, and the pattern of the sequence is defined by a rule which is applied to each successive number.These are examples of recursively defined sequences. Recursive sequences are defined by an initial term and a rule that tells how to find the next term in the sequence by using the previous term.In each of the examples, the first term is given and the rule for finding the nth term is provided.These are all examples of arithmetic sequences, in which each term is determined by the previous term.The first term in each sequence is given, and the general pattern is expressed as a(n) = x + y a(n-1), where x and y are constants.The value of a(n) can then be determined by substituting the appropriate values for n and a(n-1).To learn more about arithmetic sequences refer to:
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What is a 15 degree angle called?
Answer:Acute Angle
Step-by-step explanation:
What is a 15 degree angle called? Acute Angle – Acute Angle An acute angle is an angle that is more than 0° but less than 90°. Common examples of acute angles include: 15°, 30°, 45°, 60°, etc.
What number is 10 times greater than 44,660?
Answer:
the answer 446600 ,nice to be of help to u
Rhys wrote down four whole numbers.
The mode of the four numbers is 7
.
The median of the four numbers is 6
.
The range of the four numbers is 5
.
What are the four numbers that Rhys wrote down?
The four numbers that Rhys wrote down are 7 , 7 , 5 , 2 .
What is mean ?
mean can be defined as the ratio of sum of the observations and total number of observations.
Given ,
Rhys wrote down four whole numbers.
The mode of the four numbers is 7
The median of the four numbers is 6
The range of the four numbers is 5
The mode is 7 so atleast for 2 times it may be repeated.
so,
let another two numbers be x , y .
the numbers could be
7,7,x,y.
so given median = 6
so,
the elements will be arranged in either ascending order or descending order,
so, 7 , 7 , 5 , 2 .
median = 7+5 / 2 = 6
which satisfies the condition
Range = Greatest number - smallest number
= 7 - 2 = 5
Hence, the range also satisfies.
Therefore , the four numbers that Rhys wrote down are 7 , 7 , 5 , 2 .
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Draw a square with side length 7 cm. Predict the perimeter and the length of the diagonal of the square
0 iq kid hshshisjsjsijsjsjsdj
Solve for X, Leave in simplest radical form.
When a number under the root sign contains no square factors, it is considered to be a radical in its simplest form. The number y = 2
Solve for y, Leave in simplest radical form ?The expression x = 2
The number y = 2
Trigonometry is the study of the correlations between triangle angles and side lengths.
Sine, cosine, tangent, cosecant, sec, and cotone are the six trigonometric functions.
Suppose the angle is such that
opposite/hypotenuse = sin
neighboring / hypotenuse = cos
tan = opposite or nearby
Tan equals sin and cos.
cosec = 1 / sin
Sec = 1 / Cos
Cot = 1 + Tan
given the data,
Let ABC be the triangle.
The angles inside the triangle ABC are 45°, 45°, and 90°. The triangle ABC is a right-angled triangle.
Now, based on the illustration,
trigonometric relationships
tan θ = x / √2
Now , θ = 45°
In this case, x = 2.
Moreover, using trigonometric relationships,
base2 plus length2 = hypotenuse2
y = √ ( √2 )² + ( √2 )²
y = √4
y = 2
Consequently, x has a value of 2.
The number y = 2
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the ten numbers from $1$ to $10$ are split into two groups. the sum of the numbers in one group is $n,$ and the product of the numbers in the other group is $n.$ what is the largest possible value of $n?$
The largest possible value of n can be calculated using factorials and the largest value would be 3628800
The concept of factorials is used to calculate the value of n.
Factorials are defined as mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that if n is given as 5, then its factorial would be =5×4×3×2×1 = 120.
Factorial of n!= nx(n-1)(n-2)........x2x1
Factorials are used in mathematics or statistics to denote the possibilities of an event in an outcome.
The total numbers of the two groups = 10
The factorials of 10! = 10×9×8×7×6×5×4×3×2×1
= 3,628,800.
Therefore, The largest possible value of n can be calculated using factorials and the largest value would be 3628800
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Work out and simplify 2/7 divided by 3/4
Answer:
8/21
Step-by-step explanation:
2/7 ÷ 3/4 =
= 2/7 × 4/3
= 8/21
point K is 1/n of the way from J(4,5) to L(0,-7). what are the coordinates of K if n=4
The coordinates of K are (3, 1).
What is the coordinate point?
The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.
Point K is 1/n of the way from J(4,5) to L(0,-7). To find the coordinates of K, we can use the concept of linear interpolation.
Given two points J(x1,y1) and L(x2,y2) and a value of t, such that 0<=t<=1, the coordinates of the point K(x,y) that is t of the way from J to L is given by:
x = (1-t)x1 + tx2
y = (1-t)y1 + ty2
In this case, we know that n=4 and t = 1/4.
So the x and y coordinates of K are:
x = (1-1/4)x1 + (1/4)x2 = (3/4)x1 + (1/4)x2 = (3/4)(4) + (1/4)(0) = 3
y = (1-1/4)y1 + (1/4)y2 = (3/4)y1 + (1/4)y2 = (3/4)(5) + (1/4)(-7) = 1
Hence, the coordinates of K are (3, 1).
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A water sample shows 0.072 grams of some trace element for every cubic centimeter of water. Annabelle uses a container in the shape of a right cylinder with a radius of 8.6 cm and a height of 16.5 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Annabelle collected? Round your answer to the nearest tenth.
Annabelle has collected approximately 213.7 grams of the trace element.
What is the volume of a cylinder?
The volume of a cylinder can be calculated using the formula V=πr2(h). When determining the volume of a cylinder, you are simply finding the area of the circular base shape and then multiplying this by the height.
The container has the shape of a right cylinder, so the volume of the cylinder can be found by using the formula for the volume of a cylinder: V = πr^2 * h
Where r = radius , h = height, and π = 3.14
So, the volume of the container is:
V = 3.14 * 8.6^2 * 16.5 = 3.14 * 73.96 * 16.5 = 2959.18 cm^3
Now we can use this volume and the proportion of the trace element given in the problem to find the approximate amount of trace element Annabelle has collected:
0.072 g/cm^3 * 2959.18 cm^3 = 213.7 grams
Hence, Annabelle has collected approximately 213.7 grams of the trace element, rounded to the nearest tenth.
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When Yoni jumps as high as he can, the function h (t) = -16t2 + 10t models his height above the ground, in feet, where t is the number of seconds since he left the ground. Yoni needs to jump 2.5 feet in the air to be able to dunk a basketball. Which statement BEST explains why Yoni can or cannot dunk the basketball?
A Yoni CAN dunk the basketball because the discriminant of 0 = -16t² + 10t-2.5 is positive.
B Yoni CAN dunk the basketball because the discriminant of 0= -16t² + 10t - 2.5 is negative.
C Yoni CANNOT dunk the basketball because the discriminant of 0= -16t² + 10t - 2.5 is positive.
D Yoni CANNOT dunk the basketball because the discriminant of 0 = -16t2 + 10t-2.5 is negative.
The correct statement is D. Yoni CANNOT dunk the basketball because the discriminant of 0 = -16t² + 10t - 2.5 is negative.
How to determine the correct statementThe discriminant of a quadratic equation is the value that is inside the square root sign of the equation,
in this case: b²-4ac.
If the discriminant is positive, it means that the equation has two distinct real roots.If the discriminant is zero, it means that the equation has one real root.If the discriminant is negative, it means that the equation has no real roots.Given that
h(t) = -16t² + 10t
Height = 2.5
We have
-16t² + 10t = 2.5
This gives
0 = -16t² + 10t - 2.5
In this case, the discriminant of the equation 0 = -16t² + 10t - 2.5 is negative, which means that there are no real roots.
This means that Yoni will not reach the height of 2.5 feet because the equation has no real solutions, so he cannot dunk the basketball
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Is 7 an algebraic expression?
No, 7 is a number, not an algebraic expression.
No, 7 is a number, not an algebraic expression. An algebraic expression is a combination of numbers, variables, and mathematical operations (such as +, -, x, /) that can be evaluated to a single numerical value. Examples of algebraic expressions include 2x + 3 and 4y - 7.
Algebraic expressions can also contain exponents and roots, and can be combined using arithmetic operations. Algebraic expressions are used in many mathematical and scientific fields, and are fundamental to understanding advanced mathematical concepts such as algebra, calculus and more.
Therefore, No, No, 7 is a number, not an algebraic expression.
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Help!!! Need help please!!
Answer:
f(x) increases from -9 to -0.5 and from 3 to 5.
Step-by-step explanation:
See the attached graph.
For what value of k will the following pair of linear equations have infinitely many solutions kx 3y?
The value k = 6 satisfies both equations Kx + 3y − (K − 3) = 0 and 12x + Ky − K = 0.
What is meant by linear equations?A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
An equation that depicts a straight line on a graph is said to be linear. The "line" in the name of the equation will help you remember this. Regular Form. Standard forms for linear equations look like this: Ax + By = C.
A linear equation has the form y = mx + b in the slope-intercept notation. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0. (b).
Given
Kx + 3y −(K − 3) = 0
Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]
[tex]$$\therefore \mathrm{a}_1=\mathrm{k}, \mathrm{b}_1=3, \mathrm{c}=-(\mathrm{k}-3)$$[/tex]
12x + ky - k = 0
Comparing with [tex]$a_1 x+b_1 y+c 1=0$[/tex]
[tex]$$\therefore a_1=12, b_1=k, c=-k$$[/tex]
Since equation has infinite number of solutions
So, [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]
substitute the values in the above equation, we get
[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]
simplifying the equation, we get
[tex]$\frac{\mathrm{k}}{12}=\frac{3}{\mathrm{k}}$$[/tex]
[tex]$$\mathrm{k}^2=12 \times 3$$[/tex]
[tex]$$\mathrm{k}^2=36$$[/tex]
[tex]$$\mathrm{k}=\pm 6$$[/tex]
[tex]$\frac{3}{\mathrm{k}}=\frac{\mathrm{k}-3}{\mathrm{k}}$$[/tex]
simplifying the equation, we get
[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]
[tex]$$\mathrm{k}=\pm 6$$[/tex]
[tex]$\frac{3}{k}=\frac{k-3}{k}$$[/tex]
[tex]$$3 \mathrm{k}=\mathrm{k}(\mathrm{k}-3)$$[/tex]
simplifying the equation, we get
[tex]$$3 k=k^2-3 k$$[/tex]
[tex]$$\mathrm{k}^2-3 \mathrm{k}-3 \mathrm{k}=0$$[/tex]
[tex]$$k^2-6 k=0$$[/tex]
[tex]$$\mathrm{k}(\mathrm{k}-6)=0$$[/tex]
k = 0, 6
Therefore, k = 6 satisfies both equations.
The complete question is:
For what value of K will the following pair of linear equations have infinitely many solutions?
Kx + 3y −(K − 3) = 0
12x + Ky − K = 0
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latoya swam kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometers per hour. how fast would latoya swim if there were no current?
Latoya swims 7 kilometers per hour if there were no currents.
Latoya's speed without the current can be calculated by adding the speed she swam against the current (S-c) to the speed of the current (c). Since she swam the same distance at the same time in both cases, we know that (S-c) * t = S * t. Therefore, S = (S-c) + c. We know that the rate of the current is c = 2 Km/h and she swam 5 Km against the current, so (S-c) = 5 Km/t and S * t = 15 Km.
By substituting the values, we get S = (5 + 2) Km/t = 7 Km/t.
Complete question :
Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Latoya swim if there were no currents?
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Read the following tip ''if your answer is not among the choices, try writing it in a different form. ' For which questions on the math section of the psat could you use this tip?
This tip can be used for C. Multiple-choice questions.
The tip "If your answer is not among the choices, try writing it in a different form" is most applicable to multiple-choice questions on the math section of the PSAT.
This is because multiple-choice questions typically give a set of answer choices to select from, and if the student's calculation or solution does not match any of the choices, they can try to rewrite it in a different form that may match one of the choices.
For example, if the question asks for the solution of an equation in simplified radical form and the student's answer is in decimal form, the student can try converting their answer to simplified radical form.
This tip is not as useful for Grid-in questions, Matching sections, or Fill-in-the-blank questions since the answer is not given in multiple choices and the student needs to write the answer themselves.
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Complete question is given as:
Read the following tip. "If your answer is not among the choices, try writing it
in a different form." For which questions on the math section of the PSAT
could you use this tip?
A. Grid-in questions
B. Matching sections
4
C. Multiple-choice questions
D. Fill-in-the-blank questions
Answer:
multiple choice questions
Step-by-step explanation: